LMFDB - Embedded newform 847.2.f.w.372.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.4
Root			$1.60551 + 1.16647i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.w.148.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.613249 - 1.88739i) q^{2} +(-2.25424 + 1.63780i) q^{3} +(-1.56812 - 1.13930i) q^{4} +(-0.00832008 - 0.0256066i) q^{5} +(1.70875 + 5.25900i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.0990607 - 0.0719718i) q^{8} +(1.47215 - 4.53082i) q^{9} +O(q^{10})$	\(q+(0.613249 - 1.88739i) q^{2} +(-2.25424 + 1.63780i) q^{3} +(-1.56812 - 1.13930i) q^{4} +(-0.00832008 - 0.0256066i) q^{5} +(1.70875 + 5.25900i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.0990607 - 0.0719718i) q^{8} +(1.47215 - 4.53082i) q^{9} -0.0534317 q^{10} +5.40087 q^{12} +(-1.50835 + 4.64222i) q^{13} +(-1.60551 + 1.16647i) q^{14} +(0.0606939 + 0.0440967i) q^{15} +(-1.27302 - 3.91797i) q^{16} +(0.518771 + 1.59661i) q^{17} +(-7.64861 - 5.55704i) q^{18} +(-1.11154 + 0.807582i) q^{19} +(-0.0161268 + 0.0496332i) q^{20} +2.78639 q^{21} +8.06246 q^{23} +(-0.105431 + 0.324483i) q^{24} +(4.04450 - 2.93850i) q^{25} +(7.83667 + 5.69367i) q^{26} +(1.51887 + 4.67460i) q^{27} +(0.598967 + 1.84343i) q^{28} +(5.17218 + 3.75781i) q^{29} +(0.120448 - 0.0875106i) q^{30} +(1.23933 - 3.81425i) q^{31} -7.93050 q^{32} +3.33156 q^{34} +(-0.00832008 + 0.0256066i) q^{35} +(-7.47049 + 5.42763i) q^{36} +(-0.421528 - 0.306258i) q^{37} +(0.842568 + 2.59316i) q^{38} +(-4.20285 - 12.9351i) q^{39} +(-0.00266714 - 0.00193779i) q^{40} +(8.57456 - 6.22978i) q^{41} +(1.70875 - 5.25900i) q^{42} +3.73968 q^{43} -0.128267 q^{45} +(4.94430 - 15.2170i) q^{46} +(7.24804 - 5.26601i) q^{47} +(9.28655 + 6.74708i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-3.06580 - 9.43556i) q^{50} +(-3.78437 - 2.74951i) q^{51} +(7.65417 - 5.56108i) q^{52} +(-1.22388 + 3.76673i) q^{53} +9.75422 q^{54} -0.122446 q^{56} +(1.18302 - 3.64097i) q^{57} +(10.2643 - 7.45742i) q^{58} +(-7.87191 - 5.71928i) q^{59} +(-0.0449356 - 0.138298i) q^{60} +(2.61652 + 8.05281i) q^{61} +(-6.43895 - 4.67817i) q^{62} +(-3.85415 + 2.80020i) q^{63} +(-2.31732 + 7.13199i) q^{64} +0.131421 q^{65} +2.81285 q^{67} +(1.00553 - 3.09472i) q^{68} +(-18.1747 + 13.2047i) q^{69} +(0.0432272 + 0.0314064i) q^{70} +(0.632097 + 1.94539i) q^{71} +(-0.180259 - 0.554780i) q^{72} +(8.46987 + 6.15372i) q^{73} +(-0.836529 + 0.607774i) q^{74} +(-4.30459 + 13.2482i) q^{75} +2.66311 q^{76} -26.9908 q^{78} +(1.80936 - 5.56864i) q^{79} +(-0.0897340 + 0.0651956i) q^{80} +(0.482477 + 0.350540i) q^{81} +(-6.49967 - 20.0039i) q^{82} +(0.805136 + 2.47795i) q^{83} +(-4.36939 - 3.17455i) q^{84} +(0.0365676 - 0.0265679i) q^{85} +(2.29336 - 7.05823i) q^{86} -17.8139 q^{87} +1.21791 q^{89} +(-0.0786597 + 0.242090i) q^{90} +(3.94891 - 2.86905i) q^{91} +(-12.6429 - 9.18560i) q^{92} +(3.45325 + 10.6280i) q^{93} +(-5.49414 - 16.9092i) q^{94} +(0.0299275 + 0.0217436i) q^{95} +(17.8773 - 12.9886i) q^{96} +(1.04964 - 3.23046i) q^{97} +1.98451 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.613249	−	1.88739i	0.433632	−	1.33458i	−0.460849	−	0.887478i	$-0.652455\pi$
$2$	0.613249	−	1.88739i	0.433632	−	1.33458i	0.894482	−	0.447105i	$-0.147545\pi$
$3$	−2.25424	+	1.63780i	−1.30149	+	0.945585i	−0.999969	−	0.00787594i	$-0.997493\pi$
$3$	−2.25424	+	1.63780i	−1.30149	+	0.945585i	−0.301517	+	0.953461i	$0.597493\pi$
$4$	−1.56812	−	1.13930i	−0.784059	−	0.569652i
$5$	−0.00832008	−	0.0256066i	−0.00372085	−	0.0114516i	0.949179	−	0.314737i	$-0.101916\pi$
$5$	−0.00832008	−	0.0256066i	−0.00372085	−	0.0114516i	−0.952900	+	0.303286i	$0.901916\pi$
$6$	1.70875	+	5.25900i	0.697595	+	2.14698i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	0.0990607	−	0.0719718i	0.0350232	−	0.0254459i
$9$	1.47215	−	4.53082i	0.490718	−	1.51027i
$10$	−0.0534317			−0.0168966
$11$		0			0
$11$		0			0
$12$	5.40087			1.55910
$13$	−1.50835	+	4.64222i	−0.418341	+	1.28752i	0.490888	+	0.871223i	$0.336672\pi$
$13$	−1.50835	+	4.64222i	−0.418341	+	1.28752i	−0.909229	+	0.416297i	$0.863328\pi$
$14$	−1.60551	+	1.16647i	−0.429090	+	0.311752i
$15$	0.0606939	+	0.0440967i	0.0156711	+	0.0113857i
$16$	−1.27302	−	3.91797i	−0.318256	−	0.979492i
$17$	0.518771	+	1.59661i	0.125821	+	0.387236i	0.994050	−	0.108928i	$-0.0347417\pi$
$17$	0.518771	+	1.59661i	0.125821	+	0.387236i	−0.868229	+	0.496163i	$0.834742\pi$
$18$	−7.64861	−	5.55704i	−1.80280	−	1.30981i
$19$	−1.11154	+	0.807582i	−0.255005	+	0.185272i	−0.707942	−	0.706270i	$-0.750376\pi$
$19$	−1.11154	+	0.807582i	−0.255005	+	0.185272i	0.452937	+	0.891543i	$0.350376\pi$
$20$	−0.0161268	+	0.0496332i	−0.00360606	+	0.0110983i
$21$	2.78639			0.608041
$22$		0			0
$23$	8.06246			1.68114			0.840570	−	0.541703i	$-0.182220\pi$
$23$	8.06246			1.68114			0.840570	+	0.541703i	$0.182220\pi$
$24$	−0.105431	+	0.324483i	−0.0215210	+	0.0662349i
$25$	4.04450	−	2.93850i	0.808900	−	0.587700i
$26$	7.83667	+	5.69367i	1.53690	+	1.11662i
$27$	1.51887	+	4.67460i	0.292307	+	0.899628i
$28$	0.598967	+	1.84343i	0.113194	+	0.348376i
$29$	5.17218	+	3.75781i	0.960449	+	0.697807i	0.953255	−	0.302167i	$-0.0977101\pi$
$29$	5.17218	+	3.75781i	0.960449	+	0.697807i	0.00719396	+	0.999974i	$0.497710\pi$
$30$	0.120448	−	0.0875106i	0.0219907	−	0.0159772i
$31$	1.23933	−	3.81425i	0.222589	−	0.685060i	−0.775938	−	0.630809i	$-0.782723\pi$
$31$	1.23933	−	3.81425i	0.222589	−	0.685060i	0.998527	−	0.0542506i	$-0.0172770\pi$
$32$	−7.93050			−1.40193
$33$		0			0
$34$	3.33156			0.571358
$35$	−0.00832008	+	0.0256066i	−0.00140635	+	0.00432830i
$36$	−7.47049	+	5.42763i	−1.24508	+	0.904605i
$37$	−0.421528	−	0.306258i	−0.0692988	−	0.0503486i	0.552596	−	0.833449i	$-0.313637\pi$
$37$	−0.421528	−	0.306258i	−0.0692988	−	0.0503486i	−0.621895	+	0.783100i	$0.713637\pi$
$38$	0.842568	+	2.59316i	0.136683	+	0.420665i
$39$	−4.20285	−	12.9351i	−0.672995	−	2.07127i
$40$	−0.00266714	−	0.00193779i	−0.000421712	−	0.000306392i
$41$	8.57456	−	6.22978i	1.33912	−	0.972929i	0.339646	−	0.940553i	$-0.389693\pi$
$41$	8.57456	−	6.22978i	1.33912	−	0.972929i	0.999476	−	0.0323754i	$-0.0103072\pi$
$42$	1.70875	−	5.25900i	0.263666	−	0.811481i
$43$	3.73968			0.570296			0.285148	−	0.958483i	$-0.407957\pi$
$43$	3.73968			0.570296			0.285148	+	0.958483i	$0.407957\pi$
$44$		0			0
$45$	−0.128267			−0.0191209
$46$	4.94430	−	15.2170i	0.728997	−	2.24362i
$47$	7.24804	−	5.26601i	1.05723	−	0.768126i	0.0836598	−	0.996494i	$-0.473339\pi$
$47$	7.24804	−	5.26601i	1.05723	−	0.768126i	0.973575	+	0.228368i	$0.0733391\pi$
$48$	9.28655	+	6.74708i	1.34040	+	0.973856i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−3.06580	−	9.43556i	−0.433570	−	1.33439i
$51$	−3.78437	−	2.74951i	−0.529918	−	0.385008i
$52$	7.65417	−	5.56108i	1.06144	−	0.771183i
$53$	−1.22388	+	3.76673i	−0.168114	+	0.517400i	−0.999252	−	0.0386649i	$-0.987689\pi$
$53$	−1.22388	+	3.76673i	−0.168114	+	0.517400i	0.831139	+	0.556065i	$0.187689\pi$
$54$	9.75422			1.32738
$55$		0			0
$56$	−0.122446			−0.0163625
$57$	1.18302	−	3.64097i	0.156695	−	0.482258i
$58$	10.2643	−	7.45742i	1.34776	−	0.979207i
$59$	−7.87191	−	5.71928i	−1.02484	−	0.744587i	−0.0575670	−	0.998342i	$-0.518334\pi$
$59$	−7.87191	−	5.71928i	−1.02484	−	0.744587i	−0.967269	+	0.253755i	$0.918334\pi$
$60$	−0.0449356	−	0.138298i	−0.00580116	−	0.0178541i
$61$	2.61652	+	8.05281i	0.335011	+	1.03106i	0.966717	+	0.255849i	$0.0823549\pi$
$61$	2.61652	+	8.05281i	0.335011	+	1.03106i	−0.631706	+	0.775208i	$0.717645\pi$
$62$	−6.43895	−	4.67817i	−0.817747	−	0.594128i
$63$	−3.85415	+	2.80020i	−0.485577	+	0.352792i
$64$	−2.31732	+	7.13199i	−0.289665	+	0.891499i
$65$	0.131421			0.0163008
$66$		0			0
$67$	2.81285			0.343644			0.171822	−	0.985128i	$-0.445035\pi$
$67$	2.81285			0.343644			0.171822	+	0.985128i	$0.445035\pi$
$68$	1.00553	−	3.09472i	0.121939	−	0.375289i
$69$	−18.1747	+	13.2047i	−2.18798	+	1.58966i
$70$	0.0432272	+	0.0314064i	0.00516664	+	0.00375378i
$71$	0.632097	+	1.94539i	0.0750161	+	0.230876i	0.981533	−	0.191294i	$-0.0612685\pi$
$71$	0.632097	+	1.94539i	0.0750161	+	0.230876i	−0.906517	+	0.422170i	$0.861268\pi$
$72$	−0.180259	−	0.554780i	−0.0212437	−	0.0653814i
$73$	8.46987	+	6.15372i	0.991323	+	0.720238i	0.960210	−	0.279277i	$-0.0900949\pi$
$73$	8.46987	+	6.15372i	0.991323	+	0.720238i	0.0311128	+	0.999516i	$0.490095\pi$
$74$	−0.836529	+	0.607774i	−0.0972446	+	0.0706523i
$75$	−4.30459	+	13.2482i	−0.497051	+	1.52977i
$76$	2.66311			0.305479
$77$		0			0
$78$	−26.9908			−3.05611
$79$	1.80936	−	5.56864i	0.203569	−	0.626521i	−0.796200	−	0.605033i	$-0.793160\pi$
$79$	1.80936	−	5.56864i	0.203569	−	0.626521i	0.999769	−	0.0214875i	$-0.00684021\pi$
$80$	−0.0897340	+	0.0651956i	−0.0100326	+	0.00728909i
$81$	0.482477	+	0.350540i	0.0536086	+	0.0389489i
$82$	−6.49967	−	20.0039i	−0.717768	−	2.20906i
$83$	0.805136	+	2.47795i	0.0883752	+	0.271991i	0.985471	−	0.169846i	$-0.0543270\pi$
$83$	0.805136	+	2.47795i	0.0883752	+	0.271991i	−0.897095	+	0.441837i	$0.854327\pi$
$84$	−4.36939	−	3.17455i	−0.476740	−	0.346372i
$85$	0.0365676	−	0.0265679i	0.00396631	−	0.00288169i
$86$	2.29336	−	7.05823i	0.247299	−	0.761108i
$87$	−17.8139			−1.90985
$88$		0			0
$89$	1.21791			0.129099			0.0645493	−	0.997915i	$-0.479439\pi$
$89$	1.21791			0.129099			0.0645493	+	0.997915i	$0.479439\pi$
$90$	−0.0786597	+	0.242090i	−0.00829146	+	0.0255185i
$91$	3.94891	−	2.86905i	0.413958	−	0.300758i
$92$	−12.6429	−	9.18560i	−1.31811	−	0.957665i
$93$	3.45325	+	10.6280i	0.358085	+	1.10207i
$94$	−5.49414	−	16.9092i	−0.566677	−	1.74405i
$95$	0.0299275	+	0.0217436i	0.00307050	+	0.00223085i
$96$	17.8773	−	12.9886i	1.82459	−	1.32564i
$97$	1.04964	−	3.23046i	0.106575	−	0.328003i	−0.883522	−	0.468389i	$-0.844834\pi$
$97$	1.04964	−	3.23046i	0.106575	−	0.328003i	0.990097	+	0.140386i	$0.0448344\pi$
$98$	1.98451			0.200466
$99$		0			0
$100$	−9.69009			−0.969009
$101$	−1.25101	+	3.85021i	−0.124480	+	0.383111i	−0.993806	−	0.111129i	$-0.964553\pi$
$101$	−1.25101	+	3.85021i	−0.124480	+	0.383111i	0.869326	+	0.494239i	$0.164553\pi$
$102$	−7.51014	+	5.45644i	−0.743615	+	0.540268i
$103$	3.19802	+	2.32350i	0.315110	+	0.228941i	0.734086	−	0.679056i	$-0.237611\pi$
$103$	3.19802	+	2.32350i	0.315110	+	0.228941i	−0.418976	+	0.907997i	$0.637611\pi$
$104$	0.184691	+	0.568420i	0.0181104	+	0.0557382i
$105$	−0.0231830	−	0.0713500i	−0.00226243	−	0.00696304i
$106$	6.35873	+	4.61989i	0.617614	+	0.448723i
$107$	−8.41265	+	6.11215i	−0.813281	+	0.590883i	−0.914780	−	0.403952i	$-0.867636\pi$
$107$	−8.41265	+	6.11215i	−0.813281	+	0.590883i	0.101499	+	0.994836i	$0.467636\pi$
$108$	2.94403	−	9.06078i	0.283289	−	0.871874i
$109$	−3.77697			−0.361768			−0.180884	−	0.983504i	$-0.557896\pi$
$109$	−3.77697			−0.361768			−0.180884	+	0.983504i	$0.557896\pi$
$110$		0			0
$111$	1.45182			0.137800
$112$	−1.27302	+	3.91797i	−0.120290	+	0.370213i
$113$	−5.13619	+	3.73166i	−0.483173	+	0.351045i	−0.802553	−	0.596581i	$-0.796525\pi$
$113$	−5.13619	+	3.73166i	−0.483173	+	0.351045i	0.319380	+	0.947627i	$0.396525\pi$
$114$	−6.14642	−	4.46564i	−0.575665	−	0.418245i
$115$	−0.0670803	−	0.206452i	−0.00625527	−	0.0192517i
$116$	−3.82930	−	11.7854i	−0.355541	−	1.09424i
$117$	18.8126	+	13.6681i	1.73922	+	1.26362i
$118$	−15.6219	+	11.3500i	−1.43811	+	1.04485i
$119$	0.518771	−	1.59661i	0.0475557	−	0.146361i
$120$	0.00918610			0.000838572
$121$		0			0
$122$	16.8033			1.52130
$123$	−9.12597	+	28.0869i	−0.822861	+	2.53251i
$124$	−6.28900	+	4.56923i	−0.564769	+	0.410329i
$125$	−0.217807	−	0.158246i	−0.0194812	−	0.0141539i
$126$	2.92151	+	8.99149i	0.260269	+	0.801025i
$127$	−1.55475	−	4.78503i	−0.137962	−	0.424603i	0.858077	−	0.513521i	$-0.171659\pi$
$127$	−1.55475	−	4.78503i	−0.137962	−	0.424603i	−0.996039	+	0.0889179i	$0.971659\pi$
$128$	−0.792108	−	0.575500i	−0.0700131	−	0.0508675i
$129$	−8.43014	+	6.12486i	−0.742233	+	0.539264i
$130$	0.0805937	−	0.248042i	0.00706853	−	0.0217547i
$131$	−3.76357			−0.328825			−0.164412	−	0.986392i	$-0.552573\pi$
$131$	−3.76357			−0.328825			−0.164412	+	0.986392i	$0.552573\pi$
$132$		0			0
$133$	1.37394			0.119136
$134$	1.72498	−	5.30893i	0.149015	−	0.458622i
$135$	0.107063	−	0.0777861i	0.00921455	−	0.00669476i
$136$	0.166301	+	0.120825i	0.0142602	+	0.0103606i
$137$	5.91393	+	18.2012i	0.505261	+	1.55503i	0.800332	+	0.599557i	$0.204657\pi$
$137$	5.91393	+	18.2012i	0.505261	+	1.55503i	−0.295071	+	0.955475i	$0.595343\pi$
$138$	13.7768	+	42.4005i	1.17276	+	3.60937i
$139$	−2.84053	−	2.06376i	−0.240930	−	0.175046i	0.460767	−	0.887521i	$-0.347574\pi$
$139$	−2.84053	−	2.06376i	−0.240930	−	0.175046i	−0.701698	+	0.712475i	$0.747574\pi$
$140$	0.0422205	−	0.0306750i	0.00356828	−	0.00259251i
$141$	−7.71414	+	23.7417i	−0.649648	+	1.99941i
$142$	4.05934			0.340652
$143$		0			0
$144$	−19.6257			−1.63548
$145$	0.0531916	−	0.163707i	0.00441732	−	0.0135951i
$146$	16.8086	−	12.2121i	1.39109	−	1.01068i
$147$	−2.25424	−	1.63780i	−0.185927	−	0.135084i
$148$	0.312085	+	0.960498i	0.0256532	+	0.0789524i
$149$	−0.966119	−	2.97341i	−0.0791476	−	0.243591i	0.903652	−	0.428268i	$-0.140876\pi$
$149$	−0.966119	−	2.97341i	−0.0791476	−	0.243591i	−0.982799	+	0.184677i	$0.940876\pi$
$150$	22.3646	+	16.2488i	1.82606	+	1.32671i
$151$	−15.9550	+	11.5920i	−1.29840	+	0.943343i	−0.999939	−	0.0110780i	$-0.996474\pi$
$151$	−15.9550	+	11.5920i	−1.29840	+	0.943343i	−0.298462	+	0.954421i	$0.596474\pi$
$152$	−0.0519869	+	0.159999i	−0.00421669	+	0.0129777i
$153$	7.99769			0.646575
$154$		0			0
$155$	−0.107981			−0.00867326
$156$	−8.14639	+	25.0720i	−0.652233	+	2.00737i
$157$	18.5706	−	13.4924i	1.48210	−	1.07681i	0.505226	−	0.862987i	$-0.331409\pi$
$157$	18.5706	−	13.4924i	1.48210	−	1.07681i	0.976873	−	0.213820i	$-0.0685907\pi$
$158$	−9.40058	−	6.82992i	−0.747870	−	0.543359i
$159$	−3.41022	−	10.4956i	−0.270448	−	0.832355i
$160$	0.0659824	+	0.203073i	0.00521637	+	0.0160543i
$161$	−6.52267	−	4.73900i	−0.514058	−	0.373485i
$162$	0.957483	−	0.695652i	0.0752270	−	0.0546556i
$163$	5.86795	−	18.0597i	0.459613	−	1.41454i	−0.406019	−	0.913864i	$-0.633083\pi$
$163$	5.86795	−	18.0597i	0.459613	−	1.41454i	0.865633	−	0.500680i	$-0.166917\pi$
$164$	−20.5435			−1.60418
$165$		0			0
$166$	5.17061			0.401317
$167$	−0.933366	+	2.87260i	−0.0722260	+	0.222289i	−0.980653	−	0.195755i	$-0.937284\pi$
$167$	−0.933366	+	2.87260i	−0.0722260	+	0.222289i	0.908427	+	0.418044i	$0.137284\pi$
$168$	0.276022	−	0.200542i	0.0212956	−	0.0154721i
$169$	−8.75787	−	6.36296i	−0.673682	−	0.489459i
$170$	−0.0277189	−	0.0853099i	−0.00212594	−	0.00654297i
$171$	2.02265	+	6.22508i	0.154676	+	0.476044i
$172$	−5.86426	−	4.26064i	−0.447146	−	0.324870i
$173$	−7.14871	+	5.19384i	−0.543506	+	0.394880i	−0.825386	−	0.564569i	$-0.809042\pi$
$173$	−7.14871	+	5.19384i	−0.543506	+	0.394880i	0.281879	+	0.959450i	$0.409042\pi$
$174$	−10.9243	+	33.6216i	−0.828171	+	2.54885i
$175$	−4.99928			−0.377910
$176$		0			0
$177$	27.1122			2.03788
$178$	0.746884	−	2.29867i	0.0559813	−	0.172293i
$179$	−6.84779	+	4.97521i	−0.511828	+	0.371865i	−0.813517	−	0.581542i	$-0.802450\pi$
$179$	−6.84779	+	4.97521i	−0.511828	+	0.371865i	0.301689	+	0.953407i	$0.402450\pi$
$180$	0.201138	+	0.146135i	0.0149919	+	0.0108923i
$181$	−7.47846	−	23.0163i	−0.555869	−	1.71079i	−0.693637	−	0.720325i	$-0.743993\pi$
$181$	−7.47846	−	23.0163i	−0.555869	−	1.71079i	0.137767	−	0.990465i	$-0.456007\pi$
$182$	−2.99334	−	9.21255i	−0.221881	−	0.682880i
$183$	−19.0872	−	13.8676i	−1.41096	−	1.02512i
$184$	0.798673	−	0.580270i	0.0588790	−	0.0427781i
$185$	−0.00433507	+	0.0133420i	−0.000318721	+	0.000980922i
$186$	22.1769			1.62609
$187$		0			0
$188$	−17.3653			−1.26650
$189$	1.51887	−	4.67460i	0.110482	−	0.340027i
$190$	0.0593916	−	0.0431505i	0.00430872	−	0.00313047i
$191$	6.29996	+	4.57719i	0.455849	+	0.331194i	0.791901	−	0.610650i	$-0.209092\pi$
$191$	6.29996	+	4.57719i	0.455849	+	0.331194i	−0.336052	+	0.941844i	$0.609092\pi$
$192$	−6.45698	−	19.8725i	−0.465992	−	1.43418i
$193$	5.27296	+	16.2285i	0.379556	+	1.16815i	0.940353	+	0.340200i	$0.110495\pi$
$193$	5.27296	+	16.2285i	0.379556	+	1.16815i	−0.560797	+	0.827953i	$0.689505\pi$
$194$	−5.45343	−	3.96215i	−0.391533	−	0.284466i
$195$	−0.296254	+	0.215241i	−0.0212152	+	0.0154137i
$196$	0.598967	−	1.84343i	0.0427834	−	0.131674i
$197$	−6.05536			−0.431426			−0.215713	−	0.976457i	$-0.569208\pi$
$197$	−6.05536			−0.431426			−0.215713	+	0.976457i	$0.569208\pi$
$198$		0			0
$199$	−13.7181			−0.972451			−0.486226	−	0.873833i	$-0.661627\pi$
$199$	−13.7181			−0.972451			−0.486226	+	0.873833i	$0.661627\pi$
$200$	0.189162	−	0.582180i	0.0133757	−	0.0411663i
$201$	−6.34083	+	4.60688i	−0.447248	+	0.324945i
$202$	6.49966	+	4.72228i	0.457314	+	0.332258i
$203$	−1.97560	−	6.08026i	−0.138660	−	0.426750i
$204$	2.80181	+	8.62310i	0.196166	+	0.603737i
$205$	−0.230864	−	0.167733i	−0.0161243	−	0.0117150i
$206$	6.34652	−	4.61101i	0.442183	−	0.321265i
$207$	11.8692	−	36.5296i	0.824965	−	2.53898i
$208$	20.1082			1.39425
$209$		0			0
$210$	−0.148882			−0.0102738
$211$	5.57320	−	17.1525i	0.383675	−	1.18083i	−0.553762	−	0.832675i	$-0.686808\pi$
$211$	5.57320	−	17.1525i	0.383675	−	1.18083i	0.937437	−	0.348155i	$-0.113192\pi$
$212$	6.21065	−	4.51230i	0.426549	−	0.309906i
$213$	−4.61107	−	3.35014i	−0.315945	−	0.229548i
$214$	6.37693	+	19.6262i	0.435918	+	1.34162i
$215$	−0.0311145	−	0.0957604i	−0.00212199	−	0.00653081i
$216$	0.486900	+	0.353753i	0.0331293	+	0.0240699i
$217$	−3.24460	+	2.35734i	−0.220258	+	0.160026i
$218$	−2.31622	+	7.12860i	−0.156874	+	0.482810i
$219$	−29.1717			−1.97124
$220$		0			0
$221$	−8.19432			−0.551210
$222$	0.890325	−	2.74014i	0.0597547	−	0.183906i
$223$	5.28542	−	3.84008i	0.353938	−	0.257151i	−0.396581	−	0.918000i	$-0.629803\pi$
$223$	5.28542	−	3.84008i	0.353938	−	0.257151i	0.750519	+	0.660849i	$0.229803\pi$
$224$	6.41591	+	4.66143i	0.428681	+	0.311455i
$225$	−7.35970	−	22.6508i	−0.490647	−	1.51006i
$226$	3.89332	+	11.9824i	0.258980	+	0.797059i
$227$	−11.0089	−	7.99841i	−0.730684	−	0.530873i	0.159096	−	0.987263i	$-0.449142\pi$
$227$	−11.0089	−	7.99841i	−0.730684	−	0.530873i	−0.889780	+	0.456390i	$0.849142\pi$
$228$	−6.00329	+	4.36164i	−0.397577	+	0.288857i
$229$	−6.00144	+	18.4705i	−0.396586	+	1.22057i	0.531133	+	0.847289i	$0.321767\pi$
$229$	−6.00144	+	18.4705i	−0.396586	+	1.22057i	−0.927719	+	0.373279i	$0.878233\pi$
$230$	−0.430791			−0.0284055
$231$		0			0
$232$	0.782815			0.0513943
$233$	1.34778	−	4.14803i	0.0882959	−	0.271747i	−0.897153	−	0.441721i	$-0.854368\pi$
$233$	1.34778	−	4.14803i	0.0882959	−	0.271747i	0.985449	+	0.169974i	$0.0543683\pi$
$234$	37.3338	−	27.1246i	2.44059	−	1.77319i
$235$	−0.195149	−	0.141784i	−0.0127301	−	0.00924895i
$236$	5.82808	+	17.9370i	0.379376	+	1.16760i
$237$	5.04159	+	15.5164i	0.327486	+	1.00790i
$238$	−2.69529	−	1.95824i	−0.174710	−	0.126934i
$239$	−8.56758	+	6.22471i	−0.554191	+	0.402643i	−0.829328	−	0.558762i	$-0.811277\pi$
$239$	−8.56758	+	6.22471i	−0.554191	+	0.402643i	0.275137	+	0.961405i	$0.411277\pi$
$240$	0.0955046	−	0.293933i	0.00616479	−	0.0189733i
$241$	18.6887			1.20384			0.601921	−	0.798555i	$-0.294402\pi$
$241$	18.6887			1.20384			0.601921	+	0.798555i	$0.294402\pi$
$242$		0			0
$243$	−16.4072			−1.05252
$244$	5.07159	−	15.6088i	0.324675	−	0.999248i
$245$	0.0217822	−	0.0158257i	0.00139162	−	0.00101107i
$246$	47.4142	+	34.4485i	3.02302	+	2.19635i
$247$	−2.07238	−	6.37813i	−0.131862	−	0.405831i
$248$	−0.151750	−	0.467039i	−0.00963614	−	0.0296570i
$249$	−5.87337	−	4.26725i	−0.372210	−	0.270426i
$250$	−0.432241	+	0.314041i	−0.0273373	+	0.0198617i
$251$	5.86612	−	18.0541i	0.370266	−	1.13956i	−0.576351	−	0.817202i	$-0.695524\pi$
$251$	5.86612	−	18.0541i	0.370266	−	1.13956i	0.946617	−	0.322360i	$-0.104476\pi$
$252$	9.23404			0.581690
$253$		0			0
$254$	−9.98465			−0.626493
$255$	−0.0389191	+	0.119781i	−0.00243721	+	0.00750097i
$256$	−13.7056	+	9.95771i	−0.856601	+	0.622357i
$257$	11.0908	+	8.05797i	0.691828	+	0.502643i	0.877261	−	0.480014i	$-0.159369\pi$
$257$	11.0908	+	8.05797i	0.691828	+	0.502643i	−0.185432	+	0.982657i	$0.559369\pi$
$258$	6.39019	+	19.6670i	0.397836	+	1.22441i
$259$	0.161010	+	0.495536i	0.0100046	+	0.0307911i
$260$	−0.206083	−	0.149728i	−0.0127807	−	0.00928575i
$261$	24.6402	−	17.9021i	1.52519	−	1.10811i
$262$	−2.30801	+	7.10332i	−0.142589	+	0.438844i
$263$	16.5767			1.02217			0.511083	−	0.859531i	$-0.329244\pi$
$263$	16.5767			1.02217			0.511083	+	0.859531i	$0.329244\pi$
$264$		0			0
$265$	0.106636			0.00655059
$266$	0.842568	−	2.59316i	0.0516611	−	0.158997i
$267$	−2.74547	+	1.99470i	−0.168020	+	0.122074i
$268$	−4.41087	−	3.20469i	−0.269437	−	0.195757i
$269$	−2.64012	−	8.12546i	−0.160971	−	0.495418i	0.837746	−	0.546060i	$-0.183873\pi$
$269$	−2.64012	−	8.12546i	−0.160971	−	0.495418i	−0.998717	+	0.0506426i	$0.983873\pi$
$270$	−0.0811559	−	0.249772i	−0.00493899	−	0.0152006i
$271$	5.13364	+	3.72981i	0.311846	+	0.226570i	0.732688	−	0.680564i	$-0.238265\pi$
$271$	5.13364	+	3.72981i	0.311846	+	0.226570i	−0.420842	+	0.907134i	$0.638265\pi$
$272$	5.59507	−	4.06506i	0.339251	−	0.246480i
$273$	−4.20285	+	12.9351i	−0.254368	+	0.782865i
$274$	37.9794			2.29442
$275$		0			0
$276$	43.5443			2.62106
$277$	−7.41776	+	22.8295i	−0.445690	+	1.37169i	0.436035	+	0.899930i	$0.356382\pi$
$277$	−7.41776	+	22.8295i	−0.445690	+	1.37169i	−0.881725	+	0.471763i	$0.843618\pi$
$278$	−5.63707	+	4.09557i	−0.338089	+	0.245636i
$279$	−15.4572	−	11.2303i	−0.925400	−	0.672342i
$280$	0.00101876	+	0.00313541i	6.08824e−5	+	0.000187377i
$281$	−0.992389	−	3.05426i	−0.0592009	−	0.182202i	0.917083	−	0.398697i	$-0.130537\pi$
$281$	−0.992389	−	3.05426i	−0.0592009	−	0.182202i	−0.976284	+	0.216495i	$0.930537\pi$
$282$	40.0790	+	29.1191i	2.38667	+	1.73402i
$283$	16.8303	−	12.2279i	1.00046	−	0.726875i	0.0382710	−	0.999267i	$-0.487815\pi$
$283$	16.8303	−	12.2279i	1.00046	−	0.726875i	0.962186	+	0.272393i	$0.0878150\pi$
$284$	1.22519	−	3.77076i	0.0727018	−	0.223753i
$285$	−0.103075			−0.00610567
$286$		0			0
$287$	−10.5987			−0.625624
$288$	−11.6749	+	35.9317i	−0.687951	+	2.11730i
$289$	11.4732	−	8.33579i	0.674896	−	0.490341i
$290$	−0.276358	−	0.200786i	−0.0162283	−	0.0117906i
$291$	2.92471	+	9.00132i	0.171449	+	0.527667i
$292$	−6.27079	−	19.2995i	−0.366970	−	1.12942i
$293$	−4.46370	−	3.24307i	−0.260772	−	0.189462i	0.449715	−	0.893172i	$-0.351526\pi$
$293$	−4.46370	−	3.24307i	−0.260772	−	0.189462i	−0.710487	+	0.703710i	$0.751526\pi$
$294$	−4.47357	+	3.25024i	−0.260904	+	0.189558i
$295$	−0.0809562	+	0.249157i	−0.00471345	+	0.0145065i
$296$	−0.0637988			−0.00370823
$297$		0			0
$298$	−6.20444			−0.359414
$299$	−12.1610	+	37.4277i	−0.703289	+	2.16450i
$300$	21.8438	−	15.8704i	1.26115	−	0.916280i
$301$	−3.02547	−	2.19813i	−0.174385	−	0.126698i
$302$	12.0942	+	37.2221i	0.695942	+	2.14189i
$303$	−3.48581	−	10.7282i	−0.200254	−	0.616320i
$304$	4.57910	+	3.32691i	0.262629	+	0.190811i
$305$	0.184435	−	0.134000i	0.0105607	−	0.00767282i
$306$	4.90457	−	15.0947i	0.280376	−	0.862908i
$307$	8.60991			0.491394			0.245697	−	0.969347i	$-0.420983\pi$
$307$	8.60991			0.491394			0.245697	+	0.969347i	$0.420983\pi$
$308$		0			0
$309$	−11.0145			−0.626594
$310$	−0.0662193	+	0.203802i	−0.00376100	+	0.0115752i
$311$	−15.4731	+	11.2419i	−0.877400	+	0.637469i	−0.932562	−	0.361009i	$-0.882432\pi$
$311$	−15.4731	+	11.2419i	−0.877400	+	0.637469i	0.0551620	+	0.998477i	$0.482432\pi$
$312$	−1.34730	−	0.978868i	−0.0762756	−	0.0554175i
$313$	−0.187498	−	0.577058i	−0.0105980	−	0.0326173i	0.945618	−	0.325280i	$-0.105459\pi$
$313$	−0.187498	−	0.577058i	−0.0105980	−	0.0326173i	−0.956216	+	0.292663i	$0.905459\pi$
$314$	−14.0769	−	43.3241i	−0.794404	−	2.44492i
$315$	0.103770	+	0.0753936i	0.00584680	+	0.00424795i
$316$	−9.18166	+	6.67087i	−0.516509	+	0.375266i
$317$	−1.61085	+	4.95769i	−0.0904745	+	0.278452i	−0.986048	−	0.166462i	$-0.946766\pi$
$317$	−1.61085	+	4.95769i	−0.0904745	+	0.278452i	0.895573	+	0.444914i	$0.146766\pi$
$318$	−21.9005			−1.22812
$319$		0			0
$320$	0.201906			0.0112869
$321$	8.95364	−	27.5565i	0.499744	−	1.53805i
$322$	−12.9443	+	9.40461i	−0.721360	+	0.524098i
$323$	−1.86603	−	1.35575i	−0.103829	−	0.0754361i
$324$	−0.357209	−	1.09938i	−0.0198449	−	0.0610765i
$325$	7.54065	+	23.2077i	0.418280	+	1.28733i
$326$	−30.4871	−	22.1502i	−1.68852	−	1.22678i
$327$	8.51420	−	6.18593i	0.470836	−	0.342083i
$328$	0.401033	−	1.23425i	0.0221434	−	0.0681502i
$329$	−8.95906			−0.493929
$330$		0			0
$331$	0.669012			0.0367722			0.0183861	−	0.999831i	$-0.494147\pi$
$331$	0.669012			0.0367722			0.0183861	+	0.999831i	$0.494147\pi$
$332$	1.56060	−	4.80302i	0.0856488	−	0.263600i
$333$	−2.00816	+	1.45901i	−0.110046	+	0.0799533i
$334$	4.84933	+	3.52324i	0.265343	+	0.192783i
$335$	−0.0234031	−	0.0720274i	−0.00127865	−	0.00393527i
$336$	−3.54715	−	10.9170i	−0.193513	−	0.595571i
$337$	5.34125	+	3.88065i	0.290957	+	0.211392i	0.723682	−	0.690133i	$-0.242448\pi$
$337$	5.34125	+	3.88065i	0.290957	+	0.211392i	−0.432726	+	0.901526i	$0.642448\pi$
$338$	−17.3801	+	12.6274i	−0.945354	+	0.686840i
$339$	5.46649	−	16.8241i	0.296899	−	0.913761i
$340$	−0.0876111			−0.00475138
$341$		0			0
$342$	12.9895			0.702393
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	0.370456	−	0.269152i	0.0199736	−	0.0145117i
$345$	0.489342	+	0.355528i	0.0263453	+	0.0191410i
$346$	5.41885	+	16.6775i	0.291319	+	0.896587i
$347$	3.77005	+	11.6030i	0.202387	+	0.622882i	0.999811	+	0.0194628i	$0.00619560\pi$
$347$	3.77005	+	11.6030i	0.202387	+	0.622882i	−0.797424	+	0.603420i	$0.793804\pi$
$348$	27.9342	+	20.2954i	1.49743	+	1.08795i
$349$	0.716627	−	0.520660i	0.0383602	−	0.0278703i	−0.568440	−	0.822725i	$-0.692453\pi$
$349$	0.716627	−	0.520660i	0.0383602	−	0.0278703i	0.606800	+	0.794854i	$0.292453\pi$
$350$	−3.06580	+	9.43556i	−0.163874	+	0.504352i
$351$	−23.9915			−1.28057
$352$		0			0
$353$	5.36012			0.285291			0.142645	−	0.989774i	$-0.454439\pi$
$353$	5.36012			0.285291			0.142645	+	0.989774i	$0.454439\pi$
$354$	16.6265	−	51.1712i	0.883690	−	2.71972i
$355$	0.0445558	−	0.0323717i	0.00236477	−	0.00171811i
$356$	−1.90983	−	1.38757i	−0.101221	−	0.0735413i
$357$	1.44550	+	4.44879i	0.0765040	+	0.235455i
$358$	5.19074	+	15.9755i	0.274339	+	0.844330i
$359$	−20.9090	−	15.1913i	−1.10354	−	0.801767i	−0.121903	−	0.992542i	$-0.538900\pi$
$359$	−20.9090	−	15.1913i	−1.10354	−	0.801767i	−0.981634	+	0.190775i	$0.938900\pi$
$360$	−0.0127062	+	0.00923162i	−0.000669677	+	0.000486549i
$361$	−5.28799	+	16.2748i	−0.278315	+	0.856566i
$362$	−48.0268			−2.52423
$363$		0			0
$364$	−9.46107			−0.495895
$365$	0.0871057	−	0.268084i	0.00455932	−	0.0140321i
$366$	−37.8787	+	27.5205i	−1.97995	+	1.43852i
$367$	16.5448	+	12.0205i	0.863629	+	0.627463i	0.928870	−	0.370406i	$-0.120782\pi$
$367$	16.5448	+	12.0205i	0.863629	+	0.627463i	−0.0652408	+	0.997870i	$0.520782\pi$
$368$	−10.2637	−	31.5885i	−0.535033	−	1.64666i
$369$	−15.6030	−	48.0210i	−0.812259	−	2.49987i
$370$	0.0225230	+	0.0163639i	0.00117091	+	0.000850719i
$371$	3.20417	−	2.32797i	0.166352	−	0.120862i
$372$	6.69343	−	20.6003i	0.347038	−	1.06807i
$373$	9.39109			0.486252			0.243126	−	0.969995i	$-0.421827\pi$
$373$	9.39109			0.486252			0.243126	+	0.969995i	$0.421827\pi$
$374$		0			0
$375$	0.750163			0.0387383
$376$	0.338991	−	1.04331i	0.0174821	−	0.0538045i
$377$	−25.2460	+	18.3423i	−1.30024	+	0.944676i
$378$	−7.89133	−	5.73339i	−0.405886	−	0.294894i
$379$	−1.74160	−	5.36009i	−0.0894599	−	0.275329i	0.896310	−	0.443427i	$-0.146238\pi$
$379$	−1.74160	−	5.36009i	−0.0894599	−	0.275329i	−0.985770	+	0.168098i	$0.946238\pi$
$380$	−0.0221573	−	0.0681931i	−0.00113664	−	0.00349823i
$381$	11.3417	+	8.24024i	0.581054	+	0.422160i
$382$	12.5024	−	9.08350i	0.639677	−	0.464752i
$383$	−0.389189	+	1.19780i	−0.0198866	+	0.0612047i	−0.960507	−	0.278255i	$-0.910244\pi$
$383$	−0.389189	+	1.19780i	−0.0198866	+	0.0612047i	0.940621	+	0.339459i	$0.110244\pi$
$384$	2.72816			0.139221
$385$		0			0
$386$	33.8631			1.72359
$387$	5.50539	−	16.9438i	0.279855	−	0.861304i
$388$	−5.32643	+	3.86988i	−0.270408	+	0.196463i
$389$	4.76033	+	3.45858i	0.241358	+	0.175357i	0.701888	−	0.712287i	$-0.252341\pi$
$389$	4.76033	+	3.45858i	0.241358	+	0.175357i	−0.460530	+	0.887644i	$0.652341\pi$
$390$	0.224566	+	0.691142i	0.0113713	+	0.0349974i
$391$	4.18257	+	12.8726i	0.211522	+	0.650997i
$392$	0.0990607	+	0.0719718i	0.00500332	+	0.00363512i
$393$	8.48400	−	6.16399i	0.427961	−	0.310932i
$394$	−3.71344	+	11.4288i	−0.187080	+	0.575774i
$395$	−0.157648			−0.00793212
$396$		0			0
$397$	4.86018			0.243925			0.121963	−	0.992535i	$-0.461081\pi$
$397$	4.86018			0.243925			0.121963	+	0.992535i	$0.461081\pi$
$398$	−8.41261	+	25.8914i	−0.421686	+	1.29782i
$399$	−3.09719	+	2.25024i	−0.155054	+	0.112653i
$400$	−16.6617	−	12.1054i	−0.833085	−	0.605271i
$401$	−7.88987	−	24.2825i	−0.394001	−	1.21261i	−0.929736	−	0.368226i	$-0.879965\pi$
$401$	−7.88987	−	24.2825i	−0.394001	−	1.21261i	0.535735	−	0.844386i	$-0.320035\pi$
$402$	4.80646	+	14.7928i	0.239724	+	0.737796i
$403$	15.8373	+	11.5064i	0.788910	+	0.573177i
$404$	6.34830	−	4.61231i	0.315839	−	0.229471i
$405$	0.00496188	−	0.0152711i	0.000246558	−	0.000758827i
$406$	−12.6873			−0.629661
$407$		0			0
$408$	−0.572769			−0.0283563
$409$	6.49760	−	19.9975i	0.321285	−	0.988815i	−0.651804	−	0.758387i	$-0.725988\pi$
$409$	6.49760	−	19.9975i	0.321285	−	0.988815i	0.973090	−	0.230427i	$-0.0740124\pi$
$410$	−0.458154	+	0.332868i	−0.0226266	+	0.0164392i
$411$	−43.1413	−	31.3440i	−2.12801	−	1.54609i
$412$	−2.36770	−	7.28703i	−0.116648	−	0.359006i
$413$	3.00680	+	9.25399i	0.147955	+	0.455359i
$414$	−61.6667	−	44.8035i	−3.03075	−	2.20197i
$415$	0.0567531	−	0.0412335i	0.00278590	−	0.00202408i
$416$	11.9620	−	36.8151i	0.586484	−	1.80501i
$417$	9.78326			0.479088
$418$		0			0
$419$	−31.3141			−1.52980			−0.764898	−	0.644151i	$-0.777211\pi$
$419$	−31.3141			−1.52980			−0.764898	+	0.644151i	$0.777211\pi$
$420$	−0.0449356	+	0.138298i	−0.00219263	+	0.00674823i
$421$	−10.3462	+	7.51698i	−0.504244	+	0.366355i	−0.810636	−	0.585551i	$-0.800878\pi$
$421$	−10.3462	+	7.51698i	−0.504244	+	0.366355i	0.306391	+	0.951906i	$0.400878\pi$
$422$	−28.9557	−	21.0376i	−1.40954	−	1.02409i
$423$	−13.1891	−	40.5919i	−0.641277	−	1.97365i
$424$	0.149859	+	0.461220i	0.00727782	+	0.0223988i
$425$	6.78982	+	4.93309i	0.329355	+	0.239290i
$426$	−9.15073	+	6.64839i	−0.443354	+	0.322116i
$427$	2.61652	−	8.05281i	0.126622	−	0.389703i
$428$	20.1556			0.974258
$429$		0			0
$430$	−0.199818			−0.00963607
$431$	6.51033	−	20.0367i	0.313592	−	0.965136i	−0.662738	−	0.748851i	$-0.730606\pi$
$431$	6.51033	−	20.0367i	0.313592	−	0.965136i	0.976330	−	0.216285i	$-0.0693941\pi$
$432$	16.3814	−	11.9018i	0.788149	−	0.572624i
$433$	−30.7451	−	22.3376i	−1.47752	−	1.07348i	−0.978347	−	0.206973i	$-0.933639\pi$
$433$	−30.7451	−	22.3376i	−1.47752	−	1.07348i	−0.499169	−	0.866505i	$-0.666361\pi$
$434$	2.45946	+	7.56944i	0.118058	+	0.363345i
$435$	0.148213	+	0.456152i	0.00710625	+	0.0218708i
$436$	5.92273	+	4.30312i	0.283647	+	0.206082i
$437$	−8.96176	+	6.51110i	−0.428699	+	0.311468i
$438$	−17.8895	+	55.0582i	−0.854793	+	2.63078i
$439$	−37.7677			−1.80256			−0.901278	−	0.433241i	$-0.857370\pi$
$439$	−37.7677			−1.80256			−0.901278	+	0.433241i	$0.857370\pi$
$440$		0			0
$441$	4.76399			0.226857
$442$	−5.02516	+	15.4658i	−0.239022	+	0.735635i
$443$	0.831607	−	0.604198i	0.0395108	−	0.0287063i	−0.567855	−	0.823129i	$-0.692226\pi$
$443$	0.831607	−	0.604198i	0.0395108	−	0.0287063i	0.607365	+	0.794423i	$0.292226\pi$
$444$	−2.27662	−	1.65406i	−0.108044	−	0.0784982i
$445$	−0.0101331	−	0.0311866i	−0.000480357	−	0.00147839i
$446$	−4.00644	−	12.3306i	−0.189710	−	0.583869i
$447$	7.04772	+	5.12047i	0.333346	+	0.242190i
$448$	6.06683	−	4.40781i	0.286631	−	0.208250i
$449$	6.22153	−	19.1479i	0.293612	−	0.903645i	−0.690072	−	0.723741i	$-0.742421\pi$
$449$	6.22153	−	19.1479i	0.293612	−	0.903645i	0.983684	−	0.179904i	$-0.0575789\pi$
$450$	−47.2642			−2.22806
$451$		0			0
$452$	12.3057			0.578809
$453$	16.9810	−	52.2623i	0.797839	−	2.45550i
$454$	−21.8473	+	15.8730i	−1.02534	+	0.744955i
$455$	−0.106322	−	0.0772472i	−0.00498444	−	0.00362141i
$456$	−0.144856	−	0.445821i	−0.00678350	−	0.0208775i
$457$	−7.46140	−	22.9638i	−0.349030	−	1.07420i	−0.959391	−	0.282079i	$-0.908976\pi$
$457$	−7.46140	−	22.9638i	−0.349030	−	1.07420i	0.610362	−	0.792123i	$-0.291024\pi$
$458$	31.1807	+	22.6541i	1.45698	+	1.05856i
$459$	−6.67559	+	4.85010i	−0.311590	+	0.226383i
$460$	−0.130022	+	0.400166i	−0.00606229	+	0.0186578i
$461$	11.5885			0.539731			0.269865	−	0.962898i	$-0.413021\pi$
$461$	11.5885			0.539731			0.269865	+	0.962898i	$0.413021\pi$
$462$		0			0
$463$	21.6077			1.00419			0.502097	−	0.864811i	$-0.332562\pi$
$463$	21.6077			1.00419			0.502097	+	0.864811i	$0.332562\pi$
$464$	8.13865	−	25.0482i	0.377827	−	1.16283i
$465$	0.243415	−	0.176852i	0.0112881	−	0.00820130i
$466$	−7.00242	−	5.08756i	−0.324381	−	0.235676i
$467$	4.91799	+	15.1360i	0.227577	+	0.700411i	0.998020	+	0.0629015i	$0.0200354\pi$
$467$	4.91799	+	15.1360i	0.227577	+	0.700411i	−0.770442	+	0.637510i	$0.779965\pi$
$468$	−13.9281	−	42.8664i	−0.643829	−	1.98150i
$469$	−2.27564	−	1.65335i	−0.105079	−	0.0763446i
$470$	−0.387275	+	0.281372i	−0.0178637	+	0.0129787i
$471$	−19.7649	+	60.8300i	−0.910717	+	2.80290i
$472$	−1.19142			−0.0548397
$473$		0			0
$474$	32.3772			1.48713
$475$	−2.12255	+	6.53253i	−0.0973892	+	0.299733i
$476$	−2.63252	+	1.91264i	−0.120661	+	0.0876657i
$477$	15.2646	+	11.0904i	0.698920	+	0.507795i
$478$	6.49438	+	19.9876i	0.297046	+	0.914213i
$479$	1.63276	+	5.02511i	0.0746026	+	0.229603i	0.981404	−	0.191956i	$-0.0614830\pi$
$479$	1.63276	+	5.02511i	0.0746026	+	0.229603i	−0.906801	+	0.421559i	$0.861483\pi$
$480$	−0.481333	−	0.349709i	−0.0219698	−	0.0159620i
$481$	2.05753	−	1.49488i	0.0938153	−	0.0681608i
$482$	11.4608	−	35.2727i	0.522025	−	1.60663i
$483$	22.4652			1.02220
$484$		0			0
$485$	−0.0914540			−0.00415271
$486$	−10.0617	+	30.9668i	−0.456409	+	1.40468i
$487$	21.8965	−	15.9087i	0.992225	−	0.720894i	0.0318177	−	0.999494i	$-0.489870\pi$
$487$	21.8965	−	15.9087i	0.992225	−	0.720894i	0.960407	+	0.278600i	$0.0898704\pi$
$488$	0.838769	+	0.609401i	0.0379693	+	0.0275863i
$489$	16.3504	+	50.3214i	0.739391	+	2.27561i
$490$	−0.0165113	−	0.0508166i	−0.000745905	−	0.00229566i
$491$	−15.2095	−	11.0503i	−0.686395	−	0.498695i	0.189078	−	0.981962i	$-0.439450\pi$
$491$	−15.2095	−	11.0503i	−0.686395	−	0.498695i	−0.875473	+	0.483267i	$0.839450\pi$
$492$	46.3101	−	33.6462i	2.08782	−	1.51689i
$493$	−3.31659	+	10.2074i	−0.149372	+	0.459719i
$494$	−13.3089			−0.598795
$495$		0			0
$496$	−16.5218			−0.741851
$497$	0.632097	−	1.94539i	0.0283534	−	0.0872629i
$498$	−11.6558	+	8.46842i	−0.522308	+	0.379479i
$499$	32.1719	+	23.3743i	1.44021	+	1.04638i	0.987998	+	0.154466i	$0.0493657\pi$
$499$	32.1719	+	23.3743i	1.44021	+	1.04638i	0.452214	+	0.891909i	$0.350634\pi$
$500$	0.161256	+	0.496296i	0.00721160	+	0.0221950i
$501$	−2.60072	−	8.00421i	−0.116192	−	0.357602i
$502$	−30.4776	−	22.1433i	−1.36028	−	0.988302i
$503$	−32.8157	+	23.8420i	−1.46318	+	1.06306i	−0.480658	+	0.876908i	$0.659602\pi$
$503$	−32.8157	+	23.8420i	−1.46318	+	1.06306i	−0.982521	+	0.186154i	$0.940398\pi$
$504$	−0.180259	+	0.554780i	−0.00802937	+	0.0247119i
$505$	0.108999			0.00485040
$506$		0			0
$507$	30.1636			1.33961
$508$	−3.01357	+	9.27483i	−0.133706	+	0.411504i
$509$	12.5243	−	9.09945i	0.555131	−	0.403326i	−0.274543	−	0.961575i	$-0.588527\pi$
$509$	12.5243	−	9.09945i	0.555131	−	0.403326i	0.829674	+	0.558249i	$0.188527\pi$
$510$	0.202206	+	0.146911i	0.00895381	+	0.00650532i
$511$	−3.23520	−	9.95693i	−0.143117	−	0.440469i
$512$	9.78397	+	30.1120i	0.432395	+	1.33077i
$513$	−5.46341	−	3.96940i	−0.241216	−	0.175253i
$514$	22.0100	−	15.9912i	0.970817	−	0.705340i
$515$	0.0328890	−	0.101222i	0.00144926	−	0.00446037i
$516$	20.1975			0.889147
$517$		0			0
$518$	1.03401			0.0454317
$519$	7.60843	−	23.4163i	0.333973	−	1.02786i
$520$	0.0130186	−	0.00945859i	0.000570905	−	0.000414787i
$521$	−30.3169	−	22.0265i	−1.32821	−	0.965000i	−0.999791	−	0.0204678i	$-0.993484\pi$
$521$	−30.3169	−	22.0265i	−1.32821	−	0.965000i	−0.328418	−	0.944532i	$-0.606516\pi$
$522$	−18.6777	−	57.4840i	−0.817500	−	2.51601i
$523$	−6.43111	−	19.7929i	−0.281213	−	0.865484i	−0.987508	−	0.157567i	$-0.949635\pi$
$523$	−6.43111	−	19.7929i	−0.281213	−	0.865484i	0.706295	−	0.707917i	$-0.250365\pi$
$524$	5.90172	+	4.28785i	0.257818	+	0.187316i
$525$	11.2696	−	8.18782i	0.491844	−	0.357346i
$526$	10.1657	−	31.2867i	0.443244	−	1.36417i
$527$	6.73281			0.293286
$528$		0			0
$529$	42.0033			1.82623
$530$	0.0653943	−	0.201263i	0.00284055	−	0.00874230i
$531$	−37.5017	+	27.2466i	−1.62744	+	1.18240i
$532$	−2.15450	−	1.56534i	−0.0934094	−	0.0678659i
$533$	15.9866	+	49.2017i	0.692456	+	2.13116i
$534$	2.08111	+	6.40501i	0.0900586	+	0.277172i
$535$	0.226505	+	0.164565i	0.00979266	+	0.00711478i
$536$	0.278643	−	0.202446i	0.0120355	−	0.00874432i
$537$	7.28816	−	22.4306i	0.314507	−	0.967954i
$538$	−16.9549			−0.730979
$539$		0			0
$540$	−0.256510			−0.0110384
$541$	−5.38488	+	16.5730i	−0.231514	+	0.712528i	0.766050	+	0.642780i	$0.222219\pi$
$541$	−5.38488	+	16.5730i	−0.231514	+	0.712528i	−0.997565	+	0.0697472i	$0.977781\pi$
$542$	10.1878	−	7.40186i	0.437603	−	0.317937i
$543$	54.5544	+	39.6361i	2.34115	+	1.70095i
$544$	−4.11412	−	12.6620i	−0.176391	−	0.542877i
$545$	0.0314247	+	0.0967152i	0.00134609	+	0.00414283i
$546$	21.8360	+	15.8648i	0.934496	+	0.678951i
$547$	12.7792	−	9.28463i	0.546399	−	0.396982i	−0.280057	−	0.959983i	$-0.590353\pi$
$547$	12.7792	−	9.28463i	0.546399	−	0.396982i	0.826456	+	0.563001i	$0.190353\pi$
$548$	11.4630	−	35.2794i	0.489673	−	1.50706i
$549$	40.3378			1.72157
$550$		0			0
$551$	−8.78382			−0.374203
$552$	−0.850034	+	2.61613i	−0.0361798	+	0.111350i
$553$	−4.73697	+	3.44161i	−0.201436	+	0.146352i
$554$	38.5392	+	28.0004i	1.63737	+	1.18962i
$555$	−0.0120792	−	0.0371760i	−0.000512734	−	0.00157803i
$556$	2.10303	+	6.47245i	0.0891881	+	0.274493i
$557$	13.6199	+	9.89541i	0.577092	+	0.419282i	0.837675	−	0.546170i	$-0.183915\pi$
$557$	13.6199	+	9.89541i	0.577092	+	0.419282i	−0.260582	+	0.965452i	$0.583915\pi$
$558$	−30.6751	+	22.2868i	−1.29858	+	0.943474i
$559$	−5.64075	+	17.3604i	−0.238578	+	0.734268i
$560$	0.110917			0.00468711
$561$		0			0
$562$	−6.37315			−0.268835
$563$	−11.5666	+	35.5984i	−0.487475	+	1.50029i	0.340889	+	0.940104i	$0.389272\pi$
$563$	−11.5666	+	35.5984i	−0.487475	+	1.50029i	−0.828364	+	0.560190i	$0.810728\pi$
$564$	39.1457	−	28.4410i	1.64833	−	1.19758i
$565$	0.138289	+	0.100473i	0.00581785	+	0.00422691i
$566$	−12.7577	−	39.2640i	−0.536244	−	1.65039i
$567$	−0.184290	−	0.567186i	−0.00773945	−	0.0238196i
$568$	0.202629	+	0.147219i	0.00850214	+	0.00617717i
$569$	2.24025	−	1.62763i	0.0939160	−	0.0682340i	−0.539836	−	0.841770i	$-0.681514\pi$
$569$	2.24025	−	1.62763i	0.0939160	−	0.0682340i	0.633752	+	0.773536i	$0.281514\pi$
$570$	−0.0632109	+	0.194543i	−0.00264761	+	0.00814852i
$571$	−8.85289			−0.370482			−0.185241	−	0.982693i	$-0.559307\pi$
$571$	−8.85289			−0.370482			−0.185241	+	0.982693i	$0.559307\pi$
$572$		0			0
$573$	−21.6981			−0.906453
$574$	−6.49967	+	20.0039i	−0.271291	+	0.834947i
$575$	32.6086	−	23.6916i	1.35987	−	0.988006i
$576$	28.9023	+	20.9988i	1.20426	+	0.874949i
$577$	11.4856	+	35.3491i	0.478152	+	1.47160i	0.841659	+	0.540010i	$0.181580\pi$
$577$	11.4856	+	35.3491i	0.478152	+	1.47160i	−0.363506	+	0.931592i	$0.618420\pi$
$578$	−8.69691	−	26.7663i	−0.361744	−	1.11333i
$579$	−38.4656	−	27.9469i	−1.59857	−	1.16143i
$580$	−0.269922	+	0.196110i	−0.0112079	+	0.00814303i
$581$	0.805136	−	2.47795i	0.0334027	−	0.102803i
$582$	18.7825			0.778562
$583$		0			0
$584$	1.28193			0.0530464
$585$	0.193472	−	0.595445i	0.00799907	−	0.0246186i
$586$	−8.85829	+	6.43592i	−0.365933	+	0.265866i
$587$	28.5736	+	20.7599i	1.17936	+	0.856854i	0.992099	−	0.125457i	$-0.0400396\pi$
$587$	28.5736	+	20.7599i	1.17936	+	0.856854i	0.187259	+	0.982311i	$0.440040\pi$
$588$	1.66896	+	5.13653i	0.0688267	+	0.211827i
$589$	1.70276	+	5.24056i	0.0701610	+	0.215933i
$590$	0.420610	+	0.305591i	0.0173162	+	0.0125810i
$591$	13.6502	−	9.91747i	0.561495	−	0.407950i
$592$	−0.663294	+	2.04141i	−0.0272612	+	0.0839014i
$593$	−8.09224			−0.332308			−0.166154	−	0.986100i	$-0.553135\pi$
$593$	−8.09224			−0.332308			−0.166154	+	0.986100i	$0.553135\pi$
$594$		0			0
$595$	−0.0452000			−0.00185302
$596$	−1.87263	+	5.76336i	−0.0767058	+	0.236076i
$597$	30.9239	−	22.4675i	1.26563	−	0.919535i
$598$	63.1828	+	45.9050i	2.58374	+	1.87720i
$599$	1.18544	+	3.64841i	0.0484357	+	0.149070i	0.972349	−	0.233532i	$-0.0750282\pi$
$599$	1.18544	+	3.64841i	0.0484357	+	0.149070i	−0.923913	+	0.382601i	$0.875028\pi$
$600$	0.527079	+	1.62218i	0.0215179	+	0.0662253i
$601$	11.5986	+	8.42687i	0.473116	+	0.343739i	0.798655	−	0.601790i	$-0.205545\pi$
$601$	11.5986	+	8.42687i	0.473116	+	0.343739i	−0.325538	+	0.945529i	$0.605545\pi$
$602$	−6.00409	+	4.36222i	−0.244708	+	0.177791i
$603$	4.14094	−	12.7445i	0.168632	−	0.518997i
$604$	38.2261			1.55540
$605$		0			0
$606$	−22.3859			−0.909367
$607$	4.25781	−	13.1042i	0.172819	−	0.531883i	−0.826708	−	0.562631i	$-0.809789\pi$
$607$	4.25781	−	13.1042i	0.172819	−	0.531883i	0.999527	+	0.0307486i	$0.00978911\pi$
$608$	8.81508	−	6.40453i	0.357499	−	0.259738i
$609$	14.4117	+	10.4707i	0.583992	+	0.424295i
$610$	−0.139805	−	0.430276i	−0.00566054	−	0.0174214i
$611$	13.5134	+	41.5899i	0.546693	+	1.68255i
$612$	−12.5413	−	9.11179i	−0.506952	−	0.368322i
$613$	7.72154	−	5.61003i	0.311870	−	0.226587i	−0.420828	−	0.907140i	$-0.638261\pi$
$613$	7.72154	−	5.61003i	0.311870	−	0.226587i	0.732699	+	0.680553i	$0.238261\pi$
$614$	5.28002	−	16.2502i	0.213084	−	0.655806i
$615$	0.795137			0.0320630
$616$		0			0
$617$	−31.5153			−1.26876			−0.634379	−	0.773023i	$-0.718744\pi$
$617$	−31.5153			−1.26876			−0.634379	+	0.773023i	$0.718744\pi$
$618$	−6.75464	+	20.7887i	−0.271712	+	0.836243i
$619$	−16.6089	+	12.0671i	−0.667568	+	0.485016i	−0.869210	−	0.494443i	$-0.835372\pi$
$619$	−16.6089	+	12.0671i	−0.667568	+	0.485016i	0.201642	+	0.979459i	$0.435372\pi$
$620$	0.169327	+	0.123023i	0.00680034	+	0.00494074i
$621$	12.2458	+	37.6888i	0.491409	+	1.51240i
$622$	11.7289	+	36.0978i	0.470286	+	1.44739i
$623$	−0.985313	−	0.715872i	−0.0394757	−	0.0286808i
$624$	−45.3288	+	32.9333i	−1.81460	+	1.31839i
$625$	7.72206	−	23.7661i	0.308883	−	0.950643i
$626$	−1.20411			−0.0481261
$627$		0			0
$628$	−44.4928			−1.77546
$629$	0.270299	−	0.831896i	0.0107775	−	0.0331699i
$630$	0.205934	−	0.149620i	0.00820460	−	0.00596099i
$631$	−29.0970	−	21.1402i	−1.15833	−	0.841578i	−0.168766	−	0.985656i	$-0.553978\pi$
$631$	−29.0970	−	21.1402i	−1.15833	−	0.841578i	−0.989566	+	0.144078i	$0.953978\pi$
$632$	−0.221548	−	0.681856i	−0.00881272	−	0.0271228i
$633$	15.5291	+	47.7937i	0.617227	+	1.89963i
$634$	8.36923	+	6.08060i	0.332384	+	0.241491i
$635$	−0.109593	+	0.0796237i	−0.00434905	+	0.00315977i
$636$	−6.61004	+	20.3436i	−0.262105	+	0.806676i
$637$	−4.88112			−0.193397
$638$		0			0
$639$	9.74478			0.385498
$640$	−0.00814618	+	0.0250714i	−0.000322006	+	0.000991033i
$641$	−11.0192	+	8.00590i	−0.435232	+	0.316214i	−0.783737	−	0.621092i	$-0.786689\pi$
$641$	−11.0192	+	8.00590i	−0.435232	+	0.316214i	0.348506	+	0.937307i	$0.386689\pi$
$642$	−46.5189	−	33.7980i	−1.83595	−	1.33390i
$643$	6.79501	+	20.9129i	0.267969	+	0.824724i	0.990995	+	0.133902i	$0.0427509\pi$
$643$	6.79501	+	20.9129i	0.267969	+	0.824724i	−0.723026	+	0.690821i	$0.757249\pi$
$644$	4.82915	+	14.8626i	0.190295	+	0.585669i
$645$	0.226976	+	0.164908i	0.00893717	+	0.00649323i
$646$	−3.70317	+	2.69051i	−0.145699	+	0.105857i
$647$	−4.57971	+	14.0949i	−0.180047	+	0.554128i	−0.999828	−	0.0185496i	$-0.994095\pi$
$647$	−4.57971	+	14.0949i	−0.180047	+	0.554128i	0.819781	+	0.572677i	$0.194095\pi$
$648$	0.0730235			0.00286863
$649$		0			0
$650$	48.4262			1.89943
$651$	3.45325	−	10.6280i	0.135343	−	0.416544i
$652$	−29.7771	+	21.6343i	−1.16616	+	0.847266i
$653$	−35.0932	−	25.4967i	−1.37330	−	0.997763i	−0.997471	−	0.0710750i	$-0.977357\pi$
$653$	−35.0932	−	25.4967i	−1.37330	−	0.997763i	−0.375832	−	0.926688i	$-0.622643\pi$
$654$	−6.45391	−	19.8631i	−0.252368	−	0.776708i
$655$	0.0313132	+	0.0963722i	0.00122351	+	0.00376557i
$656$	−35.3237	−	25.6642i	−1.37916	−	1.00202i
$657$	40.3504	−	29.3163i	1.57422	−	1.14374i
$658$	−5.49414	+	16.9092i	−0.214184	+	0.659190i
$659$	42.2093			1.64424			0.822121	−	0.569313i	$-0.192791\pi$
$659$	42.2093			1.64424			0.822121	+	0.569313i	$0.192791\pi$
$660$		0			0
$661$	16.2794			0.633197			0.316599	−	0.948560i	$-0.397459\pi$
$661$	16.2794			0.633197			0.316599	+	0.948560i	$0.397459\pi$
$662$	0.410271	−	1.26268i	0.0159456	−	0.0490756i
$663$	18.4720	−	13.4207i	0.717392	−	0.521215i
$664$	0.258100	+	0.187521i	0.0100162	+	0.00727722i
$665$	−0.0114313	−	0.0351819i	−0.000443286	−	0.00136430i
$666$	1.52222	+	4.68490i	0.0589847	+	0.181536i
$667$	41.7005	+	30.2972i	1.61465	+	1.17311i
$668$	4.73640	−	3.44119i	0.183257	−	0.133144i
$669$	−5.62531	+	17.3129i	−0.217487	+	0.669357i
$670$	−0.150295			−0.00580642
$671$		0			0
$672$	−22.0975			−0.852430
$673$	−1.64103	+	5.05056i	−0.0632569	+	0.194685i	−0.977690	−	0.210052i	$-0.932637\pi$
$673$	−1.64103	+	5.05056i	−0.0632569	+	0.194685i	0.914433	+	0.404736i	$0.132637\pi$
$674$	10.5998	−	7.70120i	0.408289	−	0.296639i
$675$	19.8794	+	14.4432i	0.765158	+	0.555920i
$676$	6.48401	+	19.9557i	0.249385	+	0.767529i
$677$	−10.4431	−	32.1407i	−0.401363	−	1.23527i	−0.923894	−	0.382648i	$-0.875012\pi$
$677$	−10.4431	−	32.1407i	−0.401363	−	1.23527i	0.522532	−	0.852620i	$-0.324988\pi$
$678$	−28.4013	−	20.6348i	−1.09075	−	0.792473i
$679$	−2.74799	+	1.99653i	−0.105458	+	0.0766199i
$680$	0.00171027	−	0.00526367i	6.55858e−5	−	0.000201852i
$681$	37.9164			1.45296
$682$		0			0
$683$	−15.8834			−0.607761			−0.303880	−	0.952710i	$-0.598282\pi$
$683$	−15.8834			−0.607761			−0.303880	+	0.952710i	$0.598282\pi$
$684$	3.92050	−	12.0661i	0.149904	−	0.461358i
$685$	0.416866	−	0.302871i	0.0159276	−	0.0115721i
$686$	−1.60551	−	1.16647i	−0.0612985	−	0.0445360i
$687$	−16.7224	−	51.4662i	−0.637999	−	1.96356i
$688$	−4.76071	−	14.6520i	−0.181500	−	0.558601i
$689$	−15.6399	−	11.3631i	−0.595834	−	0.432899i
$690$	0.971107	−	0.705551i	0.0369694	−	0.0268599i
$691$	7.89151	−	24.2876i	0.300207	−	0.923942i	−0.681215	−	0.732083i	$-0.738548\pi$
$691$	7.89151	−	24.2876i	0.300207	−	0.923942i	0.981422	−	0.191859i	$-0.0614517\pi$
$692$	17.1274			0.651085
$693$		0			0
$694$	24.2113			0.919050
$695$	−0.0292125	+	0.0899068i	−0.00110809	+	0.00341036i
$696$	−1.76465	+	1.28210i	−0.0668890	+	0.0485977i
$697$	14.3948	+	10.4584i	0.545242	+	0.396141i
$698$	−0.543216	−	1.67185i	−0.0205610	−	0.0632803i
$699$	3.75544	+	11.5581i	0.142044	+	0.437166i
$700$	7.83945	+	5.69569i	0.296303	+	0.215277i
$701$	2.66600	−	1.93696i	0.100693	−	0.0731579i	−0.536299	−	0.844028i	$-0.680178\pi$
$701$	2.66600	−	1.93696i	0.100693	−	0.0731579i	0.636993	+	0.770870i	$0.280178\pi$
$702$	−14.7128	+	45.2813i	−0.555298	+	1.70903i
$703$	0.715875			0.0269997
$704$		0			0
$705$	0.672125			0.0253137
$706$	3.28709	−	10.1166i	0.123711	−	0.380744i
$707$	3.27519	−	2.37956i	0.123176	−	0.0894927i
$708$	−42.5151	−	30.8891i	−1.59782	−	1.16088i
$709$	−13.8757	−	42.7049i	−0.521111	−	1.60382i	−0.771880	−	0.635769i	$-0.780683\pi$
$709$	−13.8757	−	42.7049i	−0.521111	−	1.60382i	0.250768	−	0.968047i	$-0.419317\pi$
$710$	−0.0337740	−	0.103946i	−0.00126752	−	0.00390102i
$711$	−22.5669	−	16.3958i	−0.846323	−	0.614890i
$712$	0.120647	−	0.0876554i	0.00452145	−	0.00328503i
$713$	9.99202	−	30.7523i	0.374204	−	1.15168i
$714$	9.28304			0.347409
$715$		0			0
$716$	16.4064			0.613137
$717$	9.11855	−	28.0640i	0.340538	−	1.04807i
$718$	−41.4943	+	30.1474i	−1.54855	+	1.12509i
$719$	−2.58290	−	1.87659i	−0.0963259	−	0.0699849i	0.538580	−	0.842575i	$-0.318961\pi$
$719$	−2.58290	−	1.87659i	−0.0963259	−	0.0699849i	−0.634906	+	0.772590i	$0.718961\pi$
$720$	0.163287	+	0.502547i	0.00608536	+	0.0187288i
$721$	−1.22153	−	3.75950i	−0.0454923	−	0.140011i
$722$	27.4739	+	19.9609i	1.02247	+	0.742869i
$723$	−42.1287	+	30.6083i	−1.56678	+	1.13834i
$724$	−14.4955	+	44.6125i	−0.538721	+	1.65801i
$725$	31.9612			1.18701
$726$		0			0
$727$	20.1654			0.747891			0.373946	−	0.927451i	$-0.378005\pi$
$727$	20.1654			0.747891			0.373946	+	0.927451i	$0.378005\pi$
$728$	0.184691	−	0.568420i	0.00684510	−	0.0210670i
$729$	35.5384	−	25.8202i	1.31624	−	0.956303i
$730$	−0.452560	−	0.328804i	−0.0167500	−	0.0121696i
$731$	1.94004	+	5.97083i	0.0717550	+	0.220839i
$732$	14.1315	+	43.4921i	0.522314	+	1.60752i
$733$	15.9453	+	11.5849i	0.588952	+	0.427899i	0.841940	−	0.539571i	$-0.181413\pi$
$733$	15.9453	+	11.5849i	0.588952	+	0.427899i	−0.252988	+	0.967469i	$0.581413\pi$
$734$	32.8333	−	23.8548i	1.21190	−	0.880496i
$735$	−0.0231830	+	0.0713500i	−0.000855118	+	0.00263178i
$736$	−63.9394			−2.35684
$737$		0			0
$738$	−100.203			−3.68851
$739$	−10.6789	+	32.8662i	−0.392829	+	1.20900i	0.537811	+	0.843065i	$0.319251\pi$
$739$	−10.6789	+	32.8662i	−0.392829	+	1.20900i	−0.930640	+	0.365937i	$0.880749\pi$
$740$	0.0219985	−	0.0159828i	0.000808680	−	0.000587541i
$741$	15.1178	+	10.9837i	0.555365	+	0.403496i
$742$	−2.42882	−	7.47513i	−0.0891647	−	0.274421i
$743$	−7.98443	−	24.5735i	−0.292920	−	0.901516i	−0.983912	−	0.178653i	$-0.942826\pi$
$743$	−7.98443	−	24.5735i	−0.292920	−	0.901516i	0.690992	−	0.722862i	$-0.257174\pi$
$744$	1.10700	+	0.804281i	0.0405845	+	0.0294864i
$745$	−0.0681006	+	0.0494780i	−0.00249501	+	0.00181273i
$746$	5.75907	−	17.7246i	0.210855	−	0.648944i
$747$	12.4125			0.454148
$748$		0			0
$749$	10.3986			0.379957
$750$	0.460037	−	1.41585i	0.0167982	−	0.0516995i
$751$	28.8980	−	20.9956i	1.05450	−	0.766142i	0.0814404	−	0.996678i	$-0.474048\pi$
$751$	28.8980	−	20.9956i	1.05450	−	0.766142i	0.973064	+	0.230536i	$0.0740480\pi$
$752$	−29.8590	−	21.6938i	−1.08884	−	0.791092i
$753$	16.3453	+	50.3057i	0.595656	+	1.83324i
$754$	19.1369	+	58.8973i	0.696925	+	2.14491i
$755$	0.429578	+	0.312107i	0.0156340	+	0.0113587i
$756$	−7.70756	+	5.59987i	−0.280321	+	0.203665i
$757$	−4.57952	+	14.0943i	−0.166446	+	0.512267i	−0.999140	−	0.0414660i	$-0.986797\pi$
$757$	−4.57952	+	14.0943i	−0.166446	+	0.512267i	0.832694	+	0.553733i	$0.186797\pi$
$758$	−11.1846			−0.406242
$759$		0			0
$760$	0.00452957			0.000164305
$761$	−6.72913	+	20.7101i	−0.243931	+	0.750742i	0.751879	+	0.659301i	$0.229148\pi$
$761$	−6.72913	+	20.7101i	−0.243931	+	0.750742i	−0.995810	+	0.0914417i	$0.970852\pi$
$762$	22.5078	−	16.3529i	0.815372	−	0.592402i
$763$	3.05563	+	2.22005i	0.110621	+	0.0803711i
$764$	−4.66427	−	14.3551i	−0.168747	−	0.519351i
$765$	−0.0665414	−	0.204793i	−0.00240581	−	0.00740431i
$766$	2.02204	+	1.46910i	0.0730593	+	0.0530807i
$767$	38.4237	−	27.9165i	1.38740	−	1.00801i
$768$	14.5870	−	44.8941i	0.526363	−	1.61998i
$769$	−35.6991			−1.28734			−0.643672	−	0.765302i	$-0.722590\pi$
$769$	−35.6991			−1.28734			−0.643672	+	0.765302i	$0.722590\pi$
$770$		0			0
$771$	−38.1988			−1.37570
$772$	10.2206	−	31.4557i	0.367847	−	1.13212i
$773$	−34.4827	+	25.0531i	−1.24026	+	0.901098i	−0.997615	−	0.0690182i	$-0.978013\pi$
$773$	−34.4827	+	25.0531i	−1.24026	+	0.901098i	−0.242640	+	0.970116i	$0.578013\pi$
$774$	−28.6034	−	20.7816i	−1.02813	−	0.746979i
$775$	−6.19573	−	19.0685i	−0.222557	−	0.684961i
$776$	−0.128524	−	0.395556i	−0.00461374	−	0.0141996i
$777$	−1.17454	−	0.853356i	−0.0421365	−	0.0306140i
$778$	9.44694	−	6.86361i	0.338689	−	0.246072i
$779$	−4.49992	+	13.8493i	−0.161226	+	0.496204i
$780$	0.709786			0.0254144
$781$		0			0
$782$	26.8606			0.960533
$783$	−9.71038	+	29.8855i	−0.347021	+	1.06802i
$784$	3.33282	−	2.42144i	0.119029	−	0.0864799i
$785$	−0.500002	−	0.363273i	−0.0178458	−	0.0129658i
$786$	−6.43102	−	19.7926i	−0.229387	−	0.705980i
$787$	−14.5506	−	44.7821i	−0.518672	−	1.59631i	−0.776499	−	0.630118i	$-0.783006\pi$
$787$	−14.5506	−	44.7821i	−0.518672	−	1.59631i	0.257827	−	0.966191i	$-0.416994\pi$
$788$	9.49551	+	6.89889i	0.338263	+	0.245763i
$789$	−37.3680	+	27.1494i	−1.33033	+	0.966545i
$790$	−0.0966773	+	0.297542i	−0.00343962	+	0.0105861i
$791$	6.34869			0.225733
$792$		0			0
$793$	−41.3295			−1.46765
$794$	2.98050	−	9.17303i	0.105774	−	0.325538i
$795$	−0.240383	+	0.174648i	−0.00852550	+	0.00619414i
$796$	21.5116	+	15.6291i	0.762459	+	0.553959i
$797$	−2.31226	−	7.11641i	−0.0819045	−	0.252076i	0.901716	−	0.432329i	$-0.142308\pi$
$797$	−2.31226	−	7.11641i	−0.0819045	−	0.252076i	−0.983620	+	0.180253i	$0.942308\pi$
$798$	2.34772	+	7.22555i	0.0831086	+	0.255782i
$799$	12.1679	+	8.84046i	0.430468	+	0.312753i
$800$	−32.0749	+	23.3038i	−1.13402	+	0.823913i
$801$	1.79296	−	5.51815i	0.0633510	−	0.194974i
$802$	−50.6690			−1.78918
$803$		0			0
$804$	15.1918			0.535774
$805$	−0.0670803	+	0.206452i	−0.00236427	+	0.00727648i
$806$	31.4293	−	22.8347i	1.10705	−	0.804318i
$807$	19.2593	+	13.9927i	0.677961	+	0.492568i
$808$	0.153181	+	0.471442i	0.00538888	+	0.0165853i
$809$	10.7380	+	33.0483i	0.377529	+	1.16191i	0.941757	+	0.336295i	$0.109174\pi$
$809$	10.7380	+	33.0483i	0.377529	+	1.16191i	−0.564228	+	0.825619i	$0.690826\pi$
$810$	−0.0257796	−	0.0187300i	−0.000905803	−	0.000658104i
$811$	−10.3662	+	7.53146i	−0.364005	+	0.264465i	−0.754721	−	0.656046i	$-0.772228\pi$
$811$	−10.3662	+	7.53146i	−0.364005	+	0.264465i	0.390715	+	0.920511i	$0.372228\pi$
$812$	−3.82930	+	11.7854i	−0.134382	+	0.413585i
$813$	−17.6811			−0.620105
$814$		0			0
$815$	−0.511268			−0.0179089
$816$	−5.95488	+	18.3272i	−0.208462	+	0.641581i
$817$	−4.15681	+	3.02010i	−0.145428	+	0.105660i
$818$	−33.7584	−	24.5269i	−1.18034	−	0.857564i
$819$	−7.18576	−	22.1155i	−0.251091	−	0.772778i
$820$	0.170924	+	0.526049i	0.00596892	+	0.0183704i
$821$	43.9478	+	31.9300i	1.53379	+	1.11436i	0.954085	+	0.299538i	$0.0968324\pi$
$821$	43.9478	+	31.9300i	1.53379	+	1.11436i	0.579705	+	0.814826i	$0.303168\pi$
$822$	−85.6146	+	62.2027i	−2.98615	+	2.16957i
$823$	−6.10918	+	18.8021i	−0.212953	+	0.655401i	0.786340	+	0.617794i	$0.211973\pi$
$823$	−6.10918	+	18.8021i	−0.212953	+	0.655401i	−0.999293	+	0.0376067i	$0.988027\pi$
$824$	0.484024			0.0168618
$825$		0			0
$826$	19.3098			0.671873
$827$	3.80395	−	11.7074i	0.132276	−	0.407105i	−0.862880	−	0.505409i	$-0.831342\pi$
$827$	3.80395	−	11.7074i	0.132276	−	0.407105i	0.995156	+	0.0983040i	$0.0313418\pi$
$828$	−60.2306	+	43.7601i	−2.09316	+	1.52077i
$829$	20.8127	+	15.1213i	0.722854	+	0.525184i	0.887295	−	0.461203i	$-0.152582\pi$
$829$	20.8127	+	15.1213i	0.722854	+	0.525184i	−0.164441	+	0.986387i	$0.552582\pi$
$830$	−0.0430198	−	0.132401i	−0.00149324	−	0.00459572i
$831$	−20.6688	−	63.6120i	−0.716993	−	2.20668i
$832$	−29.6129	−	21.5151i	−1.02664	−	0.745900i
$833$	−1.35816	+	0.986762i	−0.0470575	+	0.0341893i
$834$	5.99957	−	18.4648i	0.207748	−	0.639383i
$835$	0.0813232			0.00281431
$836$		0			0
$837$	19.7125			0.681363
$838$	−19.2034	+	59.1019i	−0.663369	+	2.04164i
$839$	37.7112	−	27.3988i	1.30194	−	0.945912i	0.301963	−	0.953320i	$-0.402358\pi$
$839$	37.7112	−	27.3988i	1.30194	−	0.945912i	0.999973	+	0.00740804i	$0.00235807\pi$
$840$	−0.00743171	−	0.00539945i	−0.000256418	−	0.000186299i
$841$	3.66881	+	11.2914i	0.126511	+	0.389359i
$842$	7.84262	+	24.1371i	0.270275	+	0.831820i
$843$	7.23935	+	5.25970i	0.249336	+	0.181154i
$844$	−28.2814	+	20.5476i	−0.973485	+	0.707279i
$845$	−0.0900675	+	0.277199i	−0.00309842	+	0.00953594i
$846$	−84.7009			−2.91208
$847$		0			0
$848$	16.3160			0.560292
$849$	−17.9126	+	55.1293i	−0.614759	+	1.89203i
$850$	13.4745	−	9.78980i	0.462171	−	0.335787i
$851$	−3.39856	−	2.46920i	−0.116501	−	0.0846430i
$852$	3.41387	+	10.5068i	0.116957	+	0.359957i
$853$	−3.03109	−	9.32873i	−0.103782	−	0.319410i	0.885660	−	0.464334i	$-0.153706\pi$
$853$	−3.03109	−	9.32873i	−0.103782	−	0.319410i	−0.989443	+	0.144924i	$0.953706\pi$
$854$	−13.5942	−	9.87675i	−0.465183	−	0.337976i
$855$	0.142574	−	0.103586i	0.00487594	−	0.00354258i
$856$	−0.393460	+	1.21095i	−0.0134482	+	0.0413893i
$857$	−32.9168			−1.12442			−0.562208	−	0.826996i	$-0.690048\pi$
$857$	−32.9168			−1.12442			−0.562208	+	0.826996i	$0.690048\pi$
$858$		0			0
$859$	−28.4747			−0.971543			−0.485772	−	0.874086i	$-0.661461\pi$
$859$	−28.4747			−0.971543			−0.485772	+	0.874086i	$0.661461\pi$
$860$	−0.0603091	+	0.185612i	−0.00205652	+	0.00632933i
$861$	23.8921	−	17.3586i	0.814241	−	0.591581i
$862$	−33.8246	−	24.5750i	−1.15207	−	0.837029i
$863$	9.04709	+	27.8441i	0.307966	+	0.947823i	0.978554	+	0.205992i	$0.0660422\pi$
$863$	9.04709	+	27.8441i	0.307966	+	0.947823i	−0.670587	+	0.741831i	$0.733958\pi$
$864$	−12.0454	−	37.0720i	−0.409793	−	1.26121i
$865$	0.192474	+	0.139841i	0.00654432	+	0.00475473i
$866$	−61.0141	+	44.3293i	−2.07334	+	1.50637i
$867$	−12.2111	+	37.5818i	−0.414709	+	1.27634i
$868$	7.77363			0.263854
$869$		0			0
$870$	0.951826			0.0322699
$871$	−4.24275	+	13.0579i	−0.143760	+	0.442449i
$872$	−0.374149	+	0.271835i	−0.0126703	+	0.00920551i
$873$	−13.0914	−	9.51146i	−0.443077	−	0.321914i
$874$	6.79317	+	20.9072i	0.229782	+	0.707198i
$875$	0.0831947	+	0.256047i	0.00281250	+	0.00865597i
$876$	45.7446	+	33.2354i	1.54557	+	1.12292i
$877$	18.2858	−	13.2854i	0.617468	−	0.448617i	−0.234568	−	0.972100i	$-0.575368\pi$
$877$	18.2858	−	13.2854i	0.617468	−	0.448617i	0.852036	+	0.523483i	$0.175368\pi$
$878$	−23.1610	+	71.2823i	−0.781647	+	2.40566i
$879$	15.3738			0.518544
$880$		0			0
$881$	−35.1102			−1.18289			−0.591447	−	0.806344i	$-0.701443\pi$
$881$	−35.1102			−1.18289			−0.591447	+	0.806344i	$0.701443\pi$
$882$	2.92151	−	8.99149i	0.0983724	−	0.302759i
$883$	−12.2996	+	8.93621i	−0.413916	+	0.300727i	−0.775185	−	0.631734i	$-0.782343\pi$
$883$	−12.2996	+	8.93621i	−0.413916	+	0.300727i	0.361269	+	0.932461i	$0.382343\pi$
$884$	12.8497	+	9.33582i	0.432181	+	0.313998i
$885$	−0.225576	−	0.694251i	−0.00758264	−	0.0233370i
$886$	−0.630372	−	1.94009i	−0.0211778	−	0.0651785i
$887$	31.1728	+	22.6483i	1.04668	+	0.760457i	0.971578	−	0.236719i	$-0.0760722\pi$
$887$	31.1728	+	22.6483i	1.04668	+	0.760457i	0.0751006	+	0.997176i	$0.476072\pi$
$888$	0.143818	−	0.104490i	0.00482621	−	0.00350645i
$889$	−1.55475	+	4.78503i	−0.0521447	+	0.160485i
$890$	−0.0650753			−0.00218133
$891$		0			0
$892$	−12.6632			−0.423995
$893$	−3.80376	+	11.7068i	−0.127288	+	0.391752i
$894$	13.9863	−	10.1616i	0.467772	−	0.339856i
$895$	0.184372	+	0.133954i	0.00616288	+	0.00447760i
$896$	0.302558	+	0.931179i	0.0101078	+	0.0311085i
$897$	−33.8853	−	104.288i	−1.13140	−	3.48209i
$898$	−32.3241	−	23.4849i	−1.07867	−	0.783700i
$899$	20.7432	−	15.0708i	0.691825	−	0.502641i
$900$	−14.2653	+	43.9041i	−0.475510	+	1.46347i
$901$	−6.64893			−0.221508
$902$		0			0
$903$	10.4202			0.346764
$904$	−0.240220	+	0.739322i	−0.00798961	+	0.0245895i
$905$	−0.527148	+	0.382995i	−0.0175230	+	0.0127312i
$906$	−88.2255	−	64.0996i	−2.93110	−	2.12957i
$907$	−17.4352	−	53.6600i	−0.578926	−	1.78175i	−0.622405	−	0.782696i	$-0.713844\pi$
$907$	−17.4352	−	53.6600i	−0.578926	−	1.78175i	0.0434788	−	0.999054i	$-0.486156\pi$
$908$	8.15058	+	25.0849i	0.270486	+	0.832471i
$909$	15.6030	+	11.3362i	0.517518	+	0.375998i
$910$	−0.210997	+	0.153298i	−0.00699448	+	0.00508179i
$911$	−9.45295	+	29.0932i	−0.313190	+	0.963900i	0.663303	+	0.748351i	$0.269154\pi$
$911$	−9.45295	+	29.0932i	−0.313190	+	0.963900i	−0.976493	+	0.215549i	$0.930846\pi$
$912$	−15.7712			−0.522237
$913$		0			0
$914$	−47.9173			−1.58496
$915$	−0.196296	+	0.604136i	−0.00648934	+	0.0199721i
$916$	30.4545	−	22.1265i	1.00625	−	0.731080i
$917$	3.04480	+	2.21217i	0.100548	+	0.0730524i
$918$	5.06021	+	15.5737i	0.167012	+	0.514010i
$919$	10.1637	+	31.2806i	0.335269	+	1.03185i	0.966589	+	0.256330i	$0.0825133\pi$
$919$	10.1637	+	31.2806i	0.335269	+	1.03185i	−0.631320	+	0.775522i	$0.717487\pi$
$920$	−0.0215037	−	0.0156234i	−0.000708957	−	0.000515088i
$921$	−19.4088	+	14.1013i	−0.639542	+	0.464654i
$922$	7.10664	−	21.8720i	0.234045	−	0.720316i
$923$	−9.98437			−0.328640
$924$		0			0
$925$	−2.60481			−0.0856457
$926$	13.2509	−	40.7820i	0.435451	−	1.34018i
$927$	15.2353	−	11.0691i	0.500394	−	0.363557i
$928$	−41.0180	−	29.8013i	−1.34648	−	0.978275i
$929$	6.74665	+	20.7641i	0.221350	+	0.681246i	0.998642	+	0.0521055i	$0.0165932\pi$
$929$	6.74665	+	20.7641i	0.221350	+	0.681246i	−0.777291	+	0.629141i	$0.783407\pi$
$930$	−0.184513	−	0.567873i	−0.00605042	−	0.0186213i
$931$	−1.11154	−	0.807582i	−0.0364293	−	0.0264674i
$932$	−6.83935	+	4.96908i	−0.224030	+	0.162767i
$933$	16.4682	−	50.6838i	0.539144	−	1.65931i
$934$	31.5835			1.03344
$935$		0			0
$936$	2.84730			0.0930670
$937$	−10.8008	+	33.2416i	−0.352848	+	1.08596i	0.604398	+	0.796682i	$0.293414\pi$
$937$	−10.8008	+	33.2416i	−0.352848	+	1.08596i	−0.957247	+	0.289273i	$0.906586\pi$
$938$	−4.51604	+	3.28110i	−0.147454	+	0.107132i
$939$	1.36777	+	0.993744i	0.0446355	+	0.0324296i
$940$	0.144481	+	0.444667i	0.00471245	+	0.0145034i
$941$	−6.31028	−	19.4210i	−0.205709	−	0.633108i	−0.999684	−	0.0251567i	$-0.991992\pi$
$941$	−6.31028	−	19.4210i	−0.205709	−	0.633108i	0.793974	−	0.607951i	$-0.208008\pi$
$942$	102.689	+	74.6079i	3.34579	+	2.43086i
$943$	69.1321	−	50.2274i	2.25125	−	1.63563i
$944$	−12.3868	+	38.1227i	−0.403156	+	1.24079i
$945$	−0.132338			−0.00430494
$946$		0			0
$947$	−11.3122			−0.367597			−0.183799	−	0.982964i	$-0.558839\pi$
$947$	−11.3122			−0.367597			−0.183799	+	0.982964i	$0.558839\pi$
$948$	9.77211	−	30.0755i	0.317383	−	0.976806i
$949$	−41.3424	+	30.0370i	−1.34203	+	0.975044i
$950$	11.0278	+	8.01213i	0.357788	+	0.259948i
$951$	−4.48847	−	13.8141i	−0.145549	−	0.447952i
$952$	−0.0635213	−	0.195499i	−0.00205874	−	0.00633614i
$953$	3.68847	+	2.67983i	0.119481	+	0.0868081i	0.645921	−	0.763404i	$-0.276474\pi$
$953$	3.68847	+	2.67983i	0.119481	+	0.0868081i	−0.526440	+	0.850212i	$0.676474\pi$
$954$	30.2929	−	22.0091i	0.980769	−	0.712570i
$955$	0.0647899	−	0.199403i	0.00209655	−	0.00645252i
$956$	20.5268			0.663885
$957$		0			0
$958$	10.4856			0.338775
$959$	5.91393	−	18.2012i	0.190971	−	0.587747i
$960$	−0.455145	+	0.330682i	−0.0146897	+	0.0106727i
$961$	12.0669	+	8.76714i	0.389256	+	0.282811i
$962$	−1.55964	−	4.80009i	−0.0502849	−	0.154761i
$963$	15.3083	+	47.1142i	0.493304	+	1.51823i
$964$	−29.3060	−	21.2921i	−0.943883	−	0.685771i
$965$	0.371685	−	0.270045i	0.0119650	−	0.00869305i
$966$	13.7768	−	42.4005i	0.443260	−	1.36421i
$967$	−38.9153			−1.25143			−0.625715	−	0.780052i	$-0.715193\pi$
$967$	−38.9153			−1.25143			−0.625715	+	0.780052i	$0.715193\pi$
$968$		0			0
$969$	6.42694			0.206463
$970$	−0.0560840	+	0.172609i	−0.00180075	+	0.00554214i
$971$	−34.2545	+	24.8874i	−1.09928	+	0.798674i	−0.980942	−	0.194300i	$-0.937757\pi$
$971$	−34.2545	+	24.8874i	−1.09928	+	0.798674i	−0.118338	+	0.992973i	$0.537757\pi$
$972$	25.7285	+	18.6928i	0.825241	+	0.599573i
$973$	1.08498	+	3.33924i	0.0347830	+	0.107051i
$974$	−16.5979	−	51.0831i	−0.531832	−	1.63681i
$975$	−55.0081	−	39.9657i	−1.76167	−	1.27993i
$976$	28.2198	−	20.5028i	0.903292	−	0.656280i
$977$	11.0188	−	33.9123i	0.352522	−	1.08495i	−0.604911	−	0.796293i	$-0.706791\pi$
$977$	11.0188	−	33.9123i	0.352522	−	1.08495i	0.957433	−	0.288657i	$-0.0932088\pi$
$978$	105.003			3.35762
$979$		0			0
$980$	−0.0521874			−0.00166707
$981$	−5.56028	+	17.1128i	−0.177526	+	0.546369i
$982$	−30.1835	+	21.9296i	−0.963193	+	0.699801i
$983$	23.8832	+	17.3522i	0.761756	+	0.553448i	0.899449	−	0.437027i	$-0.143968\pi$
$983$	23.8832	+	17.3522i	0.761756	+	0.553448i	−0.137692	+	0.990475i	$0.543968\pi$
$984$	1.11744	+	3.43911i	0.0356226	+	0.109635i
$985$	0.0503810	+	0.155057i	0.00160527	+	0.00494052i
$986$	17.2314	+	12.5194i	0.548760	+	0.398698i
$987$	20.1959	−	14.6732i	0.642842	−	0.467052i
$988$	−4.01690	+	12.3627i	−0.127794	+	0.393311i
$989$	30.1511			0.958748
$990$		0			0
$991$	−30.7292			−0.976145			−0.488072	−	0.872803i	$-0.662300\pi$
$991$	−30.7292			−0.976145			−0.488072	+	0.872803i	$0.662300\pi$
$992$	−9.82848	+	30.2489i	−0.312054	+	0.960405i
$993$	−1.50811	+	1.09571i	−0.0478586	+	0.0347713i
$994$	−3.28408	−	2.38602i	−0.104165	−	0.0756800i
$995$	0.114136	+	0.351274i	0.00361835	+	0.0111361i
$996$	4.34843	+	13.3831i	0.137785	+	0.424060i
$997$	−40.4474	−	29.3868i	−1.28098	−	0.930688i	−0.281400	−	0.959590i	$-0.590799\pi$
$997$	−40.4474	−	29.3868i	−1.28098	−	0.930688i	−0.999582	+	0.0289020i	$0.990799\pi$
$998$	63.8456	−	46.3866i	2.02100	−	1.46834i
$999$	0.791389	−	2.43564i	0.0250384	−	0.0770604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.w.372.4		16
11.2	odd	10		847.2.f.x.729.4		16
11.3	even	5		77.2.f.b.15.1	✓	16
11.4	even	5		847.2.a.p.1.7		8
11.5	even	5	inner	847.2.f.w.148.4		16
11.6	odd	10		847.2.f.v.148.1		16
11.7	odd	10		847.2.a.o.1.2		8
11.8	odd	10		847.2.f.x.323.4		16
11.9	even	5		77.2.f.b.36.1	yes	16
11.10	odd	2		847.2.f.v.372.1		16
33.14	odd	10		693.2.m.i.631.4		16
33.20	odd	10		693.2.m.i.190.4		16
33.26	odd	10		7623.2.a.ct.1.2		8
33.29	even	10		7623.2.a.cw.1.7		8
77.3	odd	30		539.2.q.f.422.4		32
77.9	even	15		539.2.q.g.410.4		32
77.20	odd	10		539.2.f.e.344.1		16
77.25	even	15		539.2.q.g.422.4		32
77.31	odd	30		539.2.q.f.520.1		32
77.47	odd	30		539.2.q.f.312.1		32
77.48	odd	10		5929.2.a.bt.1.7		8
77.53	even	15		539.2.q.g.520.1		32
77.58	even	15		539.2.q.g.312.1		32
77.62	even	10		5929.2.a.bs.1.2		8
77.69	odd	10		539.2.f.e.246.1		16
77.75	odd	30		539.2.q.f.410.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.1	✓	16	11.3	even	5
77.2.f.b.36.1	yes	16	11.9	even	5
539.2.f.e.246.1		16	77.69	odd	10
539.2.f.e.344.1		16	77.20	odd	10
539.2.q.f.312.1		32	77.47	odd	30
539.2.q.f.410.4		32	77.75	odd	30
539.2.q.f.422.4		32	77.3	odd	30
539.2.q.f.520.1		32	77.31	odd	30
539.2.q.g.312.1		32	77.58	even	15
539.2.q.g.410.4		32	77.9	even	15
539.2.q.g.422.4		32	77.25	even	15
539.2.q.g.520.1		32	77.53	even	15
693.2.m.i.190.4		16	33.20	odd	10
693.2.m.i.631.4		16	33.14	odd	10
847.2.a.o.1.2		8	11.7	odd	10
847.2.a.p.1.7		8	11.4	even	5
847.2.f.v.148.1		16	11.6	odd	10
847.2.f.v.372.1		16	11.10	odd	2
847.2.f.w.148.4		16	11.5	even	5	inner
847.2.f.w.372.4		16	1.1	even	1	trivial
847.2.f.x.323.4		16	11.8	odd	10
847.2.f.x.729.4		16	11.2	odd	10
5929.2.a.bs.1.2		8	77.62	even	10
5929.2.a.bt.1.7		8	77.48	odd	10
7623.2.a.ct.1.2		8	33.26	odd	10
7623.2.a.cw.1.7		8	33.29	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)

\(f(q)\)	\(=\)	\(q+(0.613249 - 1.88739i) q^{2} +(-2.25424 + 1.63780i) q^{3} +(-1.56812 - 1.13930i) q^{4} +(-0.00832008 - 0.0256066i) q^{5} +(1.70875 + 5.25900i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.0990607 - 0.0719718i) q^{8} +(1.47215 - 4.53082i) q^{9} +O(q^{10})\)	\(q+(0.613249 - 1.88739i) q^{2} +(-2.25424 + 1.63780i) q^{3} +(-1.56812 - 1.13930i) q^{4} +(-0.00832008 - 0.0256066i) q^{5} +(1.70875 + 5.25900i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.0990607 - 0.0719718i) q^{8} +(1.47215 - 4.53082i) q^{9} -0.0534317 q^{10} +5.40087 q^{12} +(-1.50835 + 4.64222i) q^{13} +(-1.60551 + 1.16647i) q^{14} +(0.0606939 + 0.0440967i) q^{15} +(-1.27302 - 3.91797i) q^{16} +(0.518771 + 1.59661i) q^{17} +(-7.64861 - 5.55704i) q^{18} +(-1.11154 + 0.807582i) q^{19} +(-0.0161268 + 0.0496332i) q^{20} +2.78639 q^{21} +8.06246 q^{23} +(-0.105431 + 0.324483i) q^{24} +(4.04450 - 2.93850i) q^{25} +(7.83667 + 5.69367i) q^{26} +(1.51887 + 4.67460i) q^{27} +(0.598967 + 1.84343i) q^{28} +(5.17218 + 3.75781i) q^{29} +(0.120448 - 0.0875106i) q^{30} +(1.23933 - 3.81425i) q^{31} -7.93050 q^{32} +3.33156 q^{34} +(-0.00832008 + 0.0256066i) q^{35} +(-7.47049 + 5.42763i) q^{36} +(-0.421528 - 0.306258i) q^{37} +(0.842568 + 2.59316i) q^{38} +(-4.20285 - 12.9351i) q^{39} +(-0.00266714 - 0.00193779i) q^{40} +(8.57456 - 6.22978i) q^{41} +(1.70875 - 5.25900i) q^{42} +3.73968 q^{43} -0.128267 q^{45} +(4.94430 - 15.2170i) q^{46} +(7.24804 - 5.26601i) q^{47} +(9.28655 + 6.74708i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-3.06580 - 9.43556i) q^{50} +(-3.78437 - 2.74951i) q^{51} +(7.65417 - 5.56108i) q^{52} +(-1.22388 + 3.76673i) q^{53} +9.75422 q^{54} -0.122446 q^{56} +(1.18302 - 3.64097i) q^{57} +(10.2643 - 7.45742i) q^{58} +(-7.87191 - 5.71928i) q^{59} +(-0.0449356 - 0.138298i) q^{60} +(2.61652 + 8.05281i) q^{61} +(-6.43895 - 4.67817i) q^{62} +(-3.85415 + 2.80020i) q^{63} +(-2.31732 + 7.13199i) q^{64} +0.131421 q^{65} +2.81285 q^{67} +(1.00553 - 3.09472i) q^{68} +(-18.1747 + 13.2047i) q^{69} +(0.0432272 + 0.0314064i) q^{70} +(0.632097 + 1.94539i) q^{71} +(-0.180259 - 0.554780i) q^{72} +(8.46987 + 6.15372i) q^{73} +(-0.836529 + 0.607774i) q^{74} +(-4.30459 + 13.2482i) q^{75} +2.66311 q^{76} -26.9908 q^{78} +(1.80936 - 5.56864i) q^{79} +(-0.0897340 + 0.0651956i) q^{80} +(0.482477 + 0.350540i) q^{81} +(-6.49967 - 20.0039i) q^{82} +(0.805136 + 2.47795i) q^{83} +(-4.36939 - 3.17455i) q^{84} +(0.0365676 - 0.0265679i) q^{85} +(2.29336 - 7.05823i) q^{86} -17.8139 q^{87} +1.21791 q^{89} +(-0.0786597 + 0.242090i) q^{90} +(3.94891 - 2.86905i) q^{91} +(-12.6429 - 9.18560i) q^{92} +(3.45325 + 10.6280i) q^{93} +(-5.49414 - 16.9092i) q^{94} +(0.0299275 + 0.0217436i) q^{95} +(17.8773 - 12.9886i) q^{96} +(1.04964 - 3.23046i) q^{97} +1.98451 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

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