LMFDB - Embedded newform 224.2.u.c.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0564658 - 1.41309i) q^{2} +(-2.95511 - 1.22405i) q^{3} +(-1.99362 + 0.159582i) q^{4} +(-1.21151 - 2.92484i) q^{5} +(-1.56282 + 4.24494i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.338075 + 2.80815i) q^{8} +(5.11306 + 5.11306i) q^{9} +O(q^{10})$	\(q+(-0.0564658 - 1.41309i) q^{2} +(-2.95511 - 1.22405i) q^{3} +(-1.99362 + 0.159582i) q^{4} +(-1.21151 - 2.92484i) q^{5} +(-1.56282 + 4.24494i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.338075 + 2.80815i) q^{8} +(5.11306 + 5.11306i) q^{9} +(-4.06464 + 1.87712i) q^{10} +(-1.89943 + 0.786772i) q^{11} +(6.08671 + 1.96870i) q^{12} +(1.39305 - 3.36312i) q^{13} +(-1.03913 - 0.959275i) q^{14} +10.1262i q^{15} +(3.94907 - 0.636293i) q^{16} +1.19342i q^{17} +(6.93648 - 7.51391i) q^{18} +(-1.98932 + 4.80264i) q^{19} +(2.88204 + 5.63769i) q^{20} +(-2.95511 + 1.22405i) q^{21} +(1.21903 + 2.63964i) q^{22} +(-4.77774 - 4.77774i) q^{23} +(2.43826 - 8.71221i) q^{24} +(-3.55139 + 3.55139i) q^{25} +(-4.83104 - 1.77860i) q^{26} +(-5.17889 - 12.5030i) q^{27} +(-1.29686 + 1.52255i) q^{28} +(-1.61945 - 0.670798i) q^{29} +(14.3091 - 0.571782i) q^{30} -1.81899 q^{31} +(-1.12212 - 5.54444i) q^{32} +6.57608 q^{33} +(1.68641 - 0.0673876i) q^{34} +(-2.92484 - 1.21151i) q^{35} +(-11.0095 - 9.37757i) q^{36} +(3.48596 + 8.41586i) q^{37} +(6.89886 + 2.53989i) q^{38} +(-8.23324 + 8.23324i) q^{39} +(7.80380 - 4.39091i) q^{40} +(-6.87077 - 6.87077i) q^{41} +(1.89655 + 4.10671i) q^{42} +(2.37639 - 0.984335i) q^{43} +(3.66120 - 1.87164i) q^{44} +(8.76036 - 21.1494i) q^{45} +(-6.48158 + 7.02114i) q^{46} -1.33587i q^{47} +(-12.4488 - 2.95352i) q^{48} -1.00000i q^{49} +(5.21894 + 4.81788i) q^{50} +(1.46080 - 3.52669i) q^{51} +(-2.24052 + 6.92710i) q^{52} +(-5.26270 + 2.17988i) q^{53} +(-17.3753 + 8.02421i) q^{54} +(4.60236 + 4.60236i) q^{55} +(2.22472 + 1.74661i) q^{56} +(11.7573 - 11.7573i) q^{57} +(-0.856451 + 2.32630i) q^{58} +(3.13737 + 7.57428i) q^{59} +(-1.61595 - 20.1877i) q^{60} +(-4.76993 - 1.97577i) q^{61} +(0.102711 + 2.57039i) q^{62} +7.23096 q^{63} +(-7.77141 + 1.89873i) q^{64} -11.5243 q^{65} +(-0.371324 - 9.29257i) q^{66} +(-9.61034 - 3.98073i) q^{67} +(-0.190449 - 2.37923i) q^{68} +(8.27057 + 19.9669i) q^{69} +(-1.54681 + 4.20145i) q^{70} +(6.26846 - 6.26846i) q^{71} +(-12.6296 + 16.0868i) q^{72} +(0.436110 + 0.436110i) q^{73} +(11.6955 - 5.40117i) q^{74} +(14.8418 - 6.14767i) q^{75} +(3.19953 - 9.89210i) q^{76} +(-0.786772 + 1.89943i) q^{77} +(12.0992 + 11.1694i) q^{78} +4.79357i q^{79} +(-6.64538 - 10.7795i) q^{80} +21.5939i q^{81} +(-9.32102 + 10.0969i) q^{82} +(2.57761 - 6.22290i) q^{83} +(5.69604 - 2.91187i) q^{84} +(3.49056 - 1.44584i) q^{85} +(-1.52513 - 3.30247i) q^{86} +(3.96456 + 3.96456i) q^{87} +(-2.85152 - 5.06791i) q^{88} +(-8.88342 + 8.88342i) q^{89} +(-30.3806 - 11.1849i) q^{90} +(-1.39305 - 3.36312i) q^{91} +(10.2875 + 8.76257i) q^{92} +(5.37531 + 2.22652i) q^{93} +(-1.88769 + 0.0754308i) q^{94} +16.4570 q^{95} +(-3.47065 + 17.7580i) q^{96} -5.09690 q^{97} +(-1.41309 + 0.0564658i) q^{98} +(-13.7347 - 5.68912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.0564658	−	1.41309i	−0.0399274	−	0.999203i
$2$	−0.0564658	−	1.41309i	−0.0399274	−	0.999203i
$3$	−2.95511	−	1.22405i	−1.70613	−	0.706704i	−0.706134	−	0.708078i	$-0.749562\pi$
$3$	−2.95511	−	1.22405i	−1.70613	−	0.706704i	−0.999999	+	0.00137446i	$0.999562\pi$
$4$	−1.99362	+	0.159582i	−0.996812	+	0.0797911i
$5$	−1.21151	−	2.92484i	−0.541802	−	1.30803i	−0.923450	−	0.383719i	$-0.874643\pi$
$5$	−1.21151	−	2.92484i	−0.541802	−	1.30803i	0.381648	−	0.924308i	$-0.375357\pi$
$6$	−1.56282	+	4.24494i	−0.638019	+	1.73299i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.338075	+	2.80815i	0.119528	+	0.992831i
$9$	5.11306	+	5.11306i	1.70435	+	1.70435i
$10$	−4.06464	+	1.87712i	−1.28535	+	0.593596i
$11$	−1.89943	+	0.786772i	−0.572701	+	0.237221i	−0.650189	−	0.759773i	$-0.725310\pi$
$11$	−1.89943	+	0.786772i	−0.572701	+	0.237221i	0.0774876	+	0.996993i	$0.475310\pi$
$12$	6.08671	+	1.96870i	1.75708	+	0.568316i
$13$	1.39305	−	3.36312i	0.386363	−	0.932762i	−0.604341	−	0.796726i	$-0.706564\pi$
$13$	1.39305	−	3.36312i	0.386363	−	0.932762i	0.990704	−	0.136037i	$-0.0434364\pi$
$14$	−1.03913	−	0.959275i	−0.277719	−	0.256377i
$15$			10.1262i			2.61456i
$16$	3.94907	−	0.636293i	0.987267	−	0.159073i
$17$			1.19342i			0.289447i	0.989472	+	0.144724i	$0.0462293\pi$
$17$			1.19342i			0.289447i	−0.989472	+	0.144724i	$0.953771\pi$
$18$	6.93648	−	7.51391i	1.63494	−	1.77105i
$19$	−1.98932	+	4.80264i	−0.456381	+	1.10180i	0.513472	+	0.858107i	$0.328359\pi$
$19$	−1.98932	+	4.80264i	−0.456381	+	1.10180i	−0.969852	+	0.243694i	$0.921641\pi$
$20$	2.88204	+	5.63769i	0.644444	+	1.26063i
$21$	−2.95511	+	1.22405i	−0.644858	+	0.267109i
$22$	1.21903	+	2.63964i	0.259898	+	0.562773i
$23$	−4.77774	−	4.77774i	−0.996228	−	0.996228i	0.00376493	−	0.999993i	$-0.498802\pi$
$23$	−4.77774	−	4.77774i	−0.996228	−	0.996228i	−0.999993	+	0.00376493i	$0.998802\pi$
$24$	2.43826	−	8.71221i	0.497707	−	1.77837i
$25$	−3.55139	+	3.55139i	−0.710277	+	0.710277i
$26$	−4.83104	−	1.77860i	−0.947445	−	0.348812i
$27$	−5.17889	−	12.5030i	−0.996679	−	2.40620i
$28$	−1.29686	+	1.52255i	−0.245084	+	0.287734i
$29$	−1.61945	−	0.670798i	−0.300724	−	0.124564i	0.227219	−	0.973844i	$-0.427037\pi$
$29$	−1.61945	−	0.670798i	−0.300724	−	0.124564i	−0.527943	+	0.849280i	$0.677037\pi$
$30$	14.3091	−	0.571782i	2.61248	−	0.104393i
$31$	−1.81899			−0.326700			−0.163350	−	0.986568i	$-0.552230\pi$
$31$	−1.81899			−0.326700			−0.163350	+	0.986568i	$0.552230\pi$
$32$	−1.12212	−	5.54444i	−0.198366	−	0.980128i
$33$	6.57608			1.14475
$34$	1.68641	−	0.0673876i	0.289217	−	0.0115569i
$35$	−2.92484	−	1.21151i	−0.494388	−	0.204782i
$36$	−11.0095	−	9.37757i	−1.83491	−	1.56293i
$37$	3.48596	+	8.41586i	0.573089	+	1.38356i	0.898912	+	0.438128i	$0.144358\pi$
$37$	3.48596	+	8.41586i	0.573089	+	1.38356i	−0.325824	+	0.945431i	$0.605642\pi$
$38$	6.89886	+	2.53989i	1.11914	+	0.412025i
$39$	−8.23324	+	8.23324i	−1.31837	+	1.31837i
$40$	7.80380	−	4.39091i	1.23389	−	0.694263i
$41$	−6.87077	−	6.87077i	−1.07303	−	1.07303i	−0.997114	−	0.0759198i	$-0.975811\pi$
$41$	−6.87077	−	6.87077i	−1.07303	−	1.07303i	−0.0759198	−	0.997114i	$-0.524189\pi$
$42$	1.89655	+	4.10671i	0.292643	+	0.633679i
$43$	2.37639	−	0.984335i	0.362397	−	0.150110i	−0.194053	−	0.980991i	$-0.562163\pi$
$43$	2.37639	−	0.984335i	0.362397	−	0.150110i	0.556449	+	0.830881i	$0.312163\pi$
$44$	3.66120	−	1.87164i	0.551947	−	0.282161i
$45$	8.76036	−	21.1494i	1.30592	−	3.15276i
$46$	−6.48158	+	7.02114i	−0.955657	+	1.03521i
$47$		−	1.33587i		−	0.194856i	−0.995243	−	0.0974280i	$-0.968938\pi$
$47$		−	1.33587i		−	0.194856i	0.995243	−	0.0974280i	$-0.0310616\pi$
$48$	−12.4488	−	2.95352i	−1.79683	−	0.426305i
$49$		−	1.00000i		−	0.142857i
$50$	5.21894	+	4.81788i	0.738070	+	0.681351i
$51$	1.46080	−	3.52669i	0.204553	−	0.493836i
$52$	−2.24052	+	6.92710i	−0.310705	+	0.960617i
$53$	−5.26270	+	2.17988i	−0.722887	+	0.299430i	−0.713625	−	0.700528i	$-0.752948\pi$
$53$	−5.26270	+	2.17988i	−0.722887	+	0.299430i	−0.00926155	+	0.999957i	$0.502948\pi$
$54$	−17.3753	+	8.02421i	−2.36448	+	1.09196i
$55$	4.60236	+	4.60236i	0.620582	+	0.620582i
$56$	2.22472	+	1.74661i	0.297290	+	0.233400i
$57$	11.7573	−	11.7573i	1.55729	−	1.55729i
$58$	−0.856451	+	2.32630i	−0.112458	+	0.305458i
$59$	3.13737	+	7.57428i	0.408451	+	0.986088i	0.985546	+	0.169410i	$0.0541864\pi$
$59$	3.13737	+	7.57428i	0.408451	+	0.986088i	−0.577095	+	0.816677i	$0.695814\pi$
$60$	−1.61595	−	20.1877i	−0.208619	−	2.60623i
$61$	−4.76993	−	1.97577i	−0.610728	−	0.252972i	0.0558120	−	0.998441i	$-0.482225\pi$
$61$	−4.76993	−	1.97577i	−0.610728	−	0.252972i	−0.666540	+	0.745470i	$0.732225\pi$
$62$	0.102711	+	2.57039i	0.0130443	+	0.326439i
$63$	7.23096			0.911016
$64$	−7.77141	+	1.89873i	−0.971426	+	0.237341i
$65$	−11.5243			−1.42941
$66$	−0.371324	−	9.29257i	−0.0457068	−	1.14384i
$67$	−9.61034	−	3.98073i	−1.17409	−	0.486324i	−0.291547	−	0.956557i	$-0.594170\pi$
$67$	−9.61034	−	3.98073i	−1.17409	−	0.486324i	−0.882542	+	0.470233i	$0.844170\pi$
$68$	−0.190449	−	2.37923i	−0.0230953	−	0.288525i
$69$	8.27057	+	19.9669i	0.995660	+	2.40374i
$70$	−1.54681	+	4.20145i	−0.184879	+	0.502170i
$71$	6.26846	−	6.26846i	0.743929	−	0.743929i	−0.229402	−	0.973332i	$-0.573677\pi$
$71$	6.26846	−	6.26846i	0.743929	−	0.743929i	0.973332	+	0.229402i	$0.0736771\pi$
$72$	−12.6296	+	16.0868i	−1.48842	+	1.89585i
$73$	0.436110	+	0.436110i	0.0510429	+	0.0510429i	0.732167	−	0.681125i	$-0.238509\pi$
$73$	0.436110	+	0.436110i	0.0510429	+	0.0510429i	−0.681125	+	0.732167i	$0.738509\pi$
$74$	11.6955	−	5.40117i	1.35957	−	0.627874i
$75$	14.8418	−	6.14767i	1.71378	−	0.709872i
$76$	3.19953	−	9.89210i	0.367012	−	1.13470i
$77$	−0.786772	+	1.89943i	−0.0896609	+	0.216461i
$78$	12.0992	+	11.1694i	1.36996	+	1.26468i
$79$			4.79357i			0.539319i	0.962956	+	0.269660i	$0.0869112\pi$
$79$			4.79357i			0.539319i	−0.962956	+	0.269660i	$0.913089\pi$
$80$	−6.64538	−	10.7795i	−0.742976	−	1.20518i
$81$			21.5939i			2.39933i
$82$	−9.32102	+	10.0969i	−1.02933	+	1.11502i
$83$	2.57761	−	6.22290i	0.282929	−	0.683052i	−0.716972	−	0.697102i	$-0.754473\pi$
$83$	2.57761	−	6.22290i	0.282929	−	0.683052i	0.999901	+	0.0140503i	$0.00447251\pi$
$84$	5.69604	−	2.91187i	0.621489	−	0.317711i
$85$	3.49056	−	1.44584i	0.378605	−	0.156823i
$86$	−1.52513	−	3.30247i	−0.164459	−	0.356114i
$87$	3.96456	+	3.96456i	0.425046	+	0.425046i
$88$	−2.85152	−	5.06791i	−0.303973	−	0.540241i
$89$	−8.88342	+	8.88342i	−0.941641	+	0.941641i	−0.998389	−	0.0567479i	$-0.981927\pi$
$89$	−8.88342	+	8.88342i	−0.941641	+	0.941641i	0.0567479	+	0.998389i	$0.481927\pi$
$90$	−30.3806	−	11.1849i	−3.20239	−	1.17899i
$91$	−1.39305	−	3.36312i	−0.146031	−	0.352551i
$92$	10.2875	+	8.76257i	1.07254	+	0.913561i
$93$	5.37531	+	2.22652i	0.557393	+	0.230880i
$94$	−1.88769	+	0.0754308i	−0.194701	+	0.00778009i
$95$	16.4570			1.68845
$96$	−3.47065	+	17.7580i	−0.354222	+	1.81241i
$97$	−5.09690			−0.517512			−0.258756	−	0.965943i	$-0.583313\pi$
$97$	−5.09690			−0.517512			−0.258756	+	0.965943i	$0.583313\pi$
$98$	−1.41309	+	0.0564658i	−0.142743	+	0.00570391i
$99$	−13.7347	−	5.68912i	−1.38039	−	0.571778i
$100$	6.51339	−	7.64686i	0.651339	−	0.764686i
$101$	−1.37705	−	3.32450i	−0.137022	−	0.330800i	0.840443	−	0.541901i	$-0.182295\pi$
$101$	−1.37705	−	3.32450i	−0.137022	−	0.330800i	−0.977464	+	0.211101i	$0.932295\pi$
$102$	−5.06601	−	1.86510i	−0.501609	−	0.184673i
$103$	9.36506	−	9.36506i	0.922766	−	0.922766i	−0.0744578	−	0.997224i	$-0.523723\pi$
$103$	9.36506	−	9.36506i	0.922766	−	0.922766i	0.997224	+	0.0744578i	$0.0237226\pi$
$104$	9.91511	+	2.77491i	0.972256	+	0.272102i
$105$	7.16027	+	7.16027i	0.698771	+	0.698771i
$106$	3.37752	+	7.31355i	0.328054	+	0.710355i
$107$	14.5212	−	6.01490i	1.40382	−	0.581482i	0.453081	−	0.891469i	$-0.350325\pi$
$107$	14.5212	−	6.01490i	1.40382	−	0.581482i	0.950741	+	0.309987i	$0.100325\pi$
$108$	12.3200	+	24.0997i	1.18549	+	2.31900i
$109$	5.33917	−	12.8899i	0.511400	−	1.23463i	−0.431670	−	0.902032i	$-0.642075\pi$
$109$	5.33917	−	12.8899i	0.511400	−	1.23463i	0.943069	−	0.332596i	$-0.107925\pi$
$110$	6.24365	−	6.76340i	0.595309	−	0.644865i
$111$		−	29.1368i		−	2.76554i
$112$	2.34248	−	3.24234i	0.221344	−	0.306372i
$113$		−	4.53065i		−	0.426208i	−0.977030	−	0.213104i	$-0.931643\pi$
$113$		−	4.53065i		−	0.426208i	0.977030	−	0.213104i	$-0.0683572\pi$
$114$	−17.2780	−	15.9502i	−1.61823	−	1.49387i
$115$	−8.18585	+	19.7624i	−0.763334	+	1.84285i
$116$	3.33562	+	1.07888i	0.309704	+	0.100172i
$117$	24.3186	−	10.0731i	2.24826	−	0.931258i
$118$	10.5260	−	4.86106i	0.968993	−	0.447497i
$119$	0.843877	+	0.843877i	0.0773581	+	0.0773581i
$120$	−28.4358	+	3.42340i	−2.59582	+	0.312512i
$121$	−4.78933	+	4.78933i	−0.435394	+	0.435394i
$122$	−2.52260	+	6.85189i	−0.228385	+	0.620341i
$123$	11.8937	+	28.7140i	1.07242	+	2.58906i
$124$	3.62638	−	0.290278i	0.325658	−	0.0260677i
$125$	0.0655671	+	0.0271588i	0.00586450	+	0.00242915i
$126$	−0.408302	−	10.2180i	−0.0363745	−	0.910289i
$127$	−1.11721			−0.0991359			−0.0495680	−	0.998771i	$-0.515784\pi$
$127$	−1.11721			−0.0991359			−0.0495680	+	0.998771i	$0.515784\pi$
$128$	3.12189	+	10.8745i	0.275939	+	0.961175i
$129$	−8.22738			−0.724380
$130$	0.650728	+	16.2848i	0.0570726	+	1.42827i
$131$	−14.3220	−	5.93236i	−1.25132	−	0.518313i	−0.344084	−	0.938939i	$-0.611810\pi$
$131$	−14.3220	−	5.93236i	−1.25132	−	0.518313i	−0.907234	+	0.420626i	$0.861810\pi$
$132$	−13.1102	+	1.04943i	−1.14110	+	0.0913408i
$133$	1.98932	+	4.80264i	0.172496	+	0.416441i
$134$	−5.08246	+	13.8050i	−0.439058	+	1.19257i
$135$	−30.2948	+	30.2948i	−2.60736	+	2.60736i
$136$	−3.35131	+	0.403466i	−0.287372	+	0.0345969i
$137$	−13.5680	−	13.5680i	−1.15919	−	1.15919i	−0.984649	−	0.174546i	$-0.944154\pi$
$137$	−13.5680	−	13.5680i	−1.15919	−	1.15919i	−0.174546	−	0.984649i	$-0.555846\pi$
$138$	27.7480	−	12.8145i	2.36206	−	1.09084i
$139$	−9.60504	+	3.97854i	−0.814689	+	0.337455i	−0.750823	−	0.660503i	$-0.770343\pi$
$139$	−9.60504	+	3.97854i	−0.814689	+	0.337455i	−0.0638656	+	0.997959i	$0.520343\pi$
$140$	6.02436	+	1.94854i	0.509151	+	0.164681i
$141$	−1.63516	+	3.94763i	−0.137705	+	0.332450i
$142$	−9.21183	−	8.50392i	−0.773039	−	0.713633i
$143$			7.48404i			0.625847i
$144$	23.4452	+	16.9384i	1.95377	+	1.41153i
$145$			5.54930i			0.460844i
$146$	0.591636	−	0.640887i	0.0489642	−	0.0530402i
$147$	−1.22405	+	2.95511i	−0.100958	+	0.243733i
$148$	−8.29272	−	16.2218i	−0.681657	−	1.33342i
$149$	10.7880	−	4.46852i	0.883784	−	0.366075i	0.105821	−	0.994385i	$-0.466253\pi$
$149$	10.7880	−	4.46852i	0.883784	−	0.366075i	0.777963	+	0.628310i	$0.216253\pi$
$150$	−9.52524	−	20.6256i	−0.777733	−	1.68407i
$151$	−5.42374	−	5.42374i	−0.441378	−	0.441378i	0.451097	−	0.892475i	$-0.351033\pi$
$151$	−5.42374	−	5.42374i	−0.441378	−	0.441378i	−0.892475	+	0.451097i	$0.851033\pi$
$152$	−14.1591	−	3.96265i	−1.14845	−	0.321413i
$153$	−6.10204	+	6.10204i	−0.493321	+	0.493321i
$154$	2.72849	+	1.00452i	0.219868	+	0.0809467i
$155$	2.20372	+	5.32024i	0.177007	+	0.427332i
$156$	15.1001	−	17.7278i	1.20897	−	1.41936i
$157$	4.99503	+	2.06901i	0.398646	+	0.165125i	0.572994	−	0.819559i	$-0.305782\pi$
$157$	4.99503	+	2.06901i	0.398646	+	0.165125i	−0.174348	+	0.984684i	$0.555782\pi$
$158$	6.77373	−	0.270673i	0.538889	−	0.0215336i
$159$	18.2201			1.44495
$160$	−14.8571	+	9.99916i	−1.17456	+	0.790503i
$161$	−6.75675			−0.532506
$162$	30.5141	−	1.21932i	2.39741	−	0.0957988i
$163$	−3.88955	−	1.61111i	−0.304653	−	0.126192i	0.225119	−	0.974331i	$-0.427723\pi$
$163$	−3.88955	−	1.61111i	−0.304653	−	0.126192i	−0.529773	+	0.848140i	$0.677723\pi$
$164$	14.7942	+	12.6013i	1.15523	+	0.983994i
$165$	−7.96697	−	19.2340i	−0.620228	−	1.49736i
$166$	−8.93903	−	3.29100i	−0.693803	−	0.255431i
$167$	1.56365	−	1.56365i	0.120999	−	0.120999i	−0.644014	−	0.765013i	$-0.722732\pi$
$167$	1.56365	−	1.56365i	0.120999	−	0.120999i	0.765013	+	0.644014i	$0.222732\pi$
$168$	−4.43635	−	7.88457i	−0.342272	−	0.608308i
$169$	−0.177611	−	0.177611i	−0.0136624	−	0.0136624i
$170$	−2.24019	−	4.85083i	−0.171815	−	0.372041i
$171$	−34.7277	+	14.3847i	−2.65569	+	1.10002i
$172$	−4.58055	+	2.34162i	−0.349264	+	0.178547i
$173$	−2.75410	+	6.64900i	−0.209391	+	0.505514i	−0.993328	−	0.115327i	$-0.963209\pi$
$173$	−2.75410	+	6.64900i	−0.209391	+	0.505514i	0.783937	+	0.620840i	$0.213209\pi$
$174$	5.37840	−	5.82613i	0.407736	−	0.441678i
$175$			5.02242i			0.379659i
$176$	−7.00038	+	4.31561i	−0.527673	+	0.325301i
$177$		−	26.2231i		−	1.97105i
$178$	13.0546	+	12.0514i	0.978487	+	0.903292i
$179$	7.21557	−	17.4199i	0.539317	−	1.30203i	−0.385883	−	0.922548i	$-0.626103\pi$
$179$	7.21557	−	17.4199i	0.539317	−	1.30203i	0.925200	−	0.379479i	$-0.123897\pi$
$180$	−14.0898	+	43.5619i	−1.05019	+	3.24691i
$181$	−15.6146	+	6.46778i	−1.16062	+	0.480746i	−0.878083	−	0.478509i	$-0.841177\pi$
$181$	−15.6146	+	6.46778i	−1.16062	+	0.480746i	−0.282541	+	0.959255i	$0.591177\pi$
$182$	−4.67372	+	2.15840i	−0.346439	+	0.159991i
$183$	11.6772	+	11.6772i	0.863207	+	0.863207i
$184$	11.8014	−	15.0318i	0.870009	−	1.10816i
$185$	20.3917	−	20.3917i	1.49923	−	1.49923i
$186$	2.84275	−	7.72149i	0.208440	−	0.566167i
$187$	−0.938951	−	2.26683i	−0.0686629	−	0.165767i
$188$	0.213180	+	2.66321i	0.0155478	+	0.194235i
$189$	−12.5030	−	5.17889i	−0.909456	−	0.376709i
$190$	−0.929258	−	23.2551i	−0.0674155	−	1.68711i
$191$	1.01760			0.0736312			0.0368156	−	0.999322i	$-0.488279\pi$
$191$	1.01760			0.0736312			0.0368156	+	0.999322i	$0.488279\pi$
$192$	25.2895	+	3.90161i	1.82511	+	0.281575i
$193$	7.46181			0.537113			0.268557	−	0.963264i	$-0.413453\pi$
$193$	7.46181			0.537113			0.268557	+	0.963264i	$0.413453\pi$
$194$	0.287801	+	7.20236i	0.0206629	+	0.517099i
$195$	34.0555	+	14.1062i	2.43876	+	1.01017i
$196$	0.159582	+	1.99362i	0.0113987	+	0.142402i
$197$	−0.292908	−	0.707143i	−0.0208688	−	0.0503818i	0.913102	−	0.407732i	$-0.133680\pi$
$197$	−0.292908	−	0.707143i	−0.0208688	−	0.0503818i	−0.933970	+	0.357350i	$0.883680\pi$
$198$	−7.26367	+	19.7296i	−0.516206	+	1.40212i
$199$	4.45204	−	4.45204i	0.315597	−	0.315597i	−0.531476	−	0.847073i	$-0.678363\pi$
$199$	4.45204	−	4.45204i	0.315597	−	0.315597i	0.847073	+	0.531476i	$0.178363\pi$
$200$	−11.1735	−	8.77219i	−0.790083	−	0.620287i
$201$	23.5270	+	23.5270i	1.65947	+	1.65947i
$202$	−4.62004	+	2.13361i	−0.325065	+	0.150120i
$203$	−1.61945	+	0.670798i	−0.113663	+	0.0470808i
$204$	−2.34950	+	7.26402i	−0.164498	+	0.508583i
$205$	−11.7719	+	28.4199i	−0.822184	+	1.98493i
$206$	−13.7624	−	12.7048i	−0.958874	−	0.885187i
$207$		−	48.8578i		−	3.39585i
$208$	3.36132	−	14.1676i	0.233065	−	0.982345i
$209$		−	10.6874i		−	0.739265i
$210$	9.71377	−	10.5224i	0.670314	−	0.726114i
$211$	8.02053	−	19.3633i	0.552156	−	1.33302i	−0.363700	−	0.931516i	$-0.618487\pi$
$211$	8.02053	−	19.3633i	0.552156	−	1.33302i	0.915856	−	0.401507i	$-0.131513\pi$
$212$	10.1440	−	5.18569i	0.696690	−	0.356155i
$213$	−26.1969	+	10.8511i	−1.79498	+	0.743505i
$214$	−9.31952	−	20.1801i	−0.637069	−	1.37949i
$215$	−5.75804	−	5.75804i	−0.392695	−	0.392695i
$216$	33.3593	−	18.7700i	2.26981	−	1.27714i
$217$	−1.28622	+	1.28622i	−0.0873142	+	0.0873142i
$218$	−18.5160	−	6.81687i	−1.25406	−	0.461696i
$219$	−0.754935	−	1.82257i	−0.0510138	−	0.123158i
$220$	−9.90982	−	8.44091i	−0.668120	−	0.569086i
$221$	4.01362	+	1.66250i	0.269986	+	0.111832i
$222$	−41.1728	+	1.64523i	−2.76333	+	0.110421i
$223$	−1.41136			−0.0945115			−0.0472558	−	0.998883i	$-0.515048\pi$
$223$	−1.41136			−0.0945115			−0.0472558	+	0.998883i	$0.515048\pi$
$224$	−4.71397	−	3.12705i	−0.314966	−	0.208935i
$225$	−36.3169			−2.42113
$226$	−6.40219	+	0.255827i	−0.425868	+	0.0170174i
$227$	−5.68703	−	2.35565i	−0.377462	−	0.156350i	0.185883	−	0.982572i	$-0.440486\pi$
$227$	−5.68703	−	2.35565i	−0.377462	−	0.156350i	−0.563344	+	0.826222i	$0.690486\pi$
$228$	−21.5634	+	25.3159i	−1.42807	+	1.67658i
$229$	−6.15637	−	14.8628i	−0.406825	−	0.982161i	−0.985968	−	0.166936i	$-0.946613\pi$
$229$	−6.15637	−	14.8628i	−0.406825	−	0.982161i	0.579143	−	0.815226i	$-0.303387\pi$
$230$	28.3882	+	10.4514i	1.87186	+	0.689145i
$231$	4.64999	−	4.64999i	0.305947	−	0.305947i
$232$	1.33621	−	4.77444i	0.0877262	−	0.313457i
$233$	−15.3837	−	15.3837i	−1.00782	−	1.00782i	−0.999969	−	0.00784982i	$-0.997501\pi$
$233$	−15.3837	−	15.3837i	−1.00782	−	1.00782i	−0.00784982	−	0.999969i	$-0.502499\pi$
$234$	−15.6073	−	33.7955i	−1.02028	−	2.20928i
$235$	−3.90719	+	1.61841i	−0.254877	+	0.105573i
$236$	−7.46346	−	14.5996i	−0.485830	−	0.950353i
$237$	5.86756	−	14.1655i	0.381139	−	0.920150i
$238$	1.14482	−	1.24012i	0.0742077	−	0.0803851i
$239$			13.8698i			0.897165i	0.893741	+	0.448583i	$0.148071\pi$
$239$			13.8698i			0.897165i	−0.893741	+	0.448583i	$0.851929\pi$
$240$	6.44321	+	39.9889i	0.415907	+	2.58127i
$241$			11.6377i			0.749648i	0.927096	+	0.374824i	$0.122297\pi$
$241$			11.6377i			0.749648i	−0.927096	+	0.374824i	$0.877703\pi$
$242$	7.03817	+	6.49730i	0.452431	+	0.417662i
$243$	10.8953	−	26.3035i	0.698933	−	1.68737i
$244$	9.82475	+	3.17775i	0.628965	+	0.203434i
$245$	−2.92484	+	1.21151i	−0.186861	+	0.0774003i
$246$	39.9038	−	18.4282i	2.54417	−	1.17494i
$247$	13.3806	+	13.3806i	0.851389	+	0.851389i
$248$	−0.614954	−	5.10799i	−0.0390496	−	0.324358i
$249$	−15.2342	+	15.2342i	−0.965430	+	0.965430i
$250$	0.0346754	−	0.0941855i	0.00219306	−	0.00595681i
$251$	9.77967	+	23.6102i	0.617288	+	1.49026i	0.854841	+	0.518890i	$0.173654\pi$
$251$	9.77967	+	23.6102i	0.617288	+	1.49026i	−0.237554	+	0.971374i	$0.576346\pi$
$252$	−14.4158	+	1.15393i	−0.908111	+	0.0726909i
$253$	12.8340	+	5.31602i	0.806867	+	0.334215i
$254$	0.0630839	+	1.57871i	0.00395824	+	0.0990569i
$255$	−12.0848			−0.756778
$256$	15.1903	−	5.02553i	0.949391	−	0.314096i
$257$	2.85163			0.177880			0.0889398	−	0.996037i	$-0.471652\pi$
$257$	2.85163			0.177880			0.0889398	+	0.996037i	$0.471652\pi$
$258$	0.464566	+	11.6260i	0.0289226	+	0.723802i
$259$	8.41586	+	3.48596i	0.522936	+	0.216607i
$260$	22.9751	−	1.83907i	1.42485	−	0.114054i
$261$	−4.85051	−	11.7102i	−0.300239	−	0.724842i
$262$	−7.57423	+	20.5732i	−0.467938	+	1.27101i
$263$	−9.56355	+	9.56355i	−0.589714	+	0.589714i	−0.937554	−	0.347840i	$-0.886915\pi$
$263$	−9.56355	+	9.56355i	−0.589714	+	0.589714i	0.347840	+	0.937554i	$0.386915\pi$
$264$	2.22321	+	18.4666i	0.136829	+	1.13654i
$265$	12.7516	+	12.7516i	0.783324	+	0.783324i
$266$	6.67421	−	3.08226i	0.409222	−	0.188985i
$267$	37.1252	−	15.3778i	2.27203	−	0.941104i
$268$	19.7946	+	6.40244i	1.20915	+	0.391091i
$269$	2.27600	−	5.49474i	0.138770	−	0.335020i	−0.839182	−	0.543851i	$-0.816966\pi$
$269$	2.27600	−	5.49474i	0.138770	−	0.335020i	0.977952	+	0.208830i	$0.0669657\pi$
$270$	44.5198	+	41.0986i	2.70939	+	2.50118i
$271$		−	13.6025i		−	0.826291i	−0.910665	−	0.413146i	$-0.864430\pi$
$271$		−	13.6025i		−	0.826291i	0.910665	−	0.413146i	$-0.135570\pi$
$272$	0.759367	+	4.71290i	0.0460434	+	0.285762i
$273$			11.6436i			0.704700i
$274$	−18.4067	+	19.9389i	−1.11199	+	1.20455i
$275$	3.95150	−	9.53975i	0.238284	−	0.575269i
$276$	−19.6748	−	38.4867i	−1.18428	−	2.31663i
$277$	17.2735	−	7.15491i	1.03786	−	0.429897i	0.202318	−	0.979320i	$-0.435152\pi$
$277$	17.2735	−	7.15491i	1.03786	−	0.429897i	0.835544	+	0.549423i	$0.185152\pi$
$278$	6.16437	+	13.3481i	0.369714	+	0.800565i
$279$	−9.30059	−	9.30059i	−0.556812	−	0.556812i
$280$	2.41328	−	8.62296i	0.144221	−	0.515320i
$281$	0.694367	−	0.694367i	0.0414225	−	0.0414225i	−0.686092	−	0.727515i	$-0.740675\pi$
$281$	0.694367	−	0.694367i	0.0414225	−	0.0414225i	0.727515	+	0.686092i	$0.240675\pi$
$282$	5.67067	+	2.08772i	0.337683	+	0.124322i
$283$	−8.05332	−	19.4424i	−0.478720	−	1.15573i	−0.960209	−	0.279281i	$-0.909904\pi$
$283$	−8.05332	−	19.4424i	−0.478720	−	1.15573i	0.481489	−	0.876452i	$-0.340096\pi$
$284$	−11.4966	+	13.4973i	−0.682199	+	0.800916i
$285$	−48.6322	−	20.1441i	−2.88072	−	1.19323i
$286$	10.5756	−	0.422593i	0.625348	−	0.0249884i
$287$	−9.71673			−0.573561
$288$	22.6116	−	34.0866i	1.33240	−	2.00857i
$289$	15.5757			0.916220
$290$	7.84164	−	0.313346i	0.460477	−	0.0184003i
$291$	15.0619	+	6.23885i	0.882945	+	0.365728i
$292$	−0.939035	−	0.799844i	−0.0549529	−	0.0468074i
$293$	9.63029	+	23.2496i	0.562608	+	1.35825i	0.907674	+	0.419676i	$0.137856\pi$
$293$	9.63029	+	23.2496i	0.562608	+	1.35825i	−0.345066	+	0.938578i	$0.612144\pi$
$294$	4.24494	+	1.56282i	0.247570	+	0.0911455i
$295$	18.3526	−	18.3526i	1.06853	−	1.06853i
$296$	−22.4545	+	12.6343i	−1.30514	+	0.734354i
$297$	19.6739	+	19.6739i	1.14160	+	1.14160i
$298$	−6.92355	−	14.9920i	−0.401071	−	0.868463i
$299$	−22.7238	+	9.41249i	−1.31415	+	0.544338i
$300$	−28.6079	+	14.6246i	−1.65168	+	0.844353i
$301$	0.984335	−	2.37639i	0.0567361	−	0.136973i
$302$	−7.35795	+	7.97047i	−0.423403	+	0.458649i
$303$			11.5098i			0.661222i
$304$	−4.80006	+	20.2317i	−0.275302	+	1.16037i
$305$			16.3449i			0.935908i
$306$	8.96727	+	8.27815i	0.512624	+	0.473230i
$307$	−7.55249	+	18.2333i	−0.431043	+	1.04063i	0.547909	+	0.836538i	$0.315424\pi$
$307$	−7.55249	+	18.2333i	−0.431043	+	1.04063i	−0.978952	+	0.204092i	$0.934576\pi$
$308$	1.26541	−	3.91231i	0.0721034	−	0.222925i
$309$	−39.1380	+	16.2115i	−2.22648	+	0.922240i
$310$	7.39352	−	3.41445i	0.419924	−	0.193928i
$311$	18.5436	+	18.5436i	1.05151	+	1.05151i	0.998599	+	0.0529146i	$0.0168511\pi$
$311$	18.5436	+	18.5436i	1.05151	+	1.05151i	0.0529146	+	0.998599i	$0.483149\pi$
$312$	−25.9036	−	20.3367i	−1.46650	−	1.15134i
$313$	21.2453	−	21.2453i	1.20086	−	1.20086i	0.226950	−	0.973906i	$-0.427125\pi$
$313$	21.2453	−	21.2453i	1.20086	−	1.20086i	0.973906	−	0.226950i	$-0.0728753\pi$
$314$	2.64164	−	7.17523i	0.149076	−	0.404922i
$315$	−8.76036	−	21.1494i	−0.493590	−	1.19163i
$316$	−0.764969	−	9.55658i	−0.0430329	−	0.537600i
$317$	−13.7411	−	5.69177i	−0.771779	−	0.319681i	−0.0381863	−	0.999271i	$-0.512158\pi$
$317$	−13.7411	−	5.69177i	−0.771779	−	0.319681i	−0.733593	+	0.679589i	$0.762158\pi$
$318$	−1.02881	−	25.7466i	−0.0576930	−	1.44380i
$319$	3.60380			0.201774
$320$	14.9686	+	20.4298i	0.836770	+	1.14206i
$321$	−50.2744			−2.80604
$322$	0.381525	+	9.54786i	0.0212616	+	0.532082i
$323$	−5.73157	−	2.37409i	−0.318913	−	0.132098i
$324$	−3.44601	−	43.0502i	−0.191445	−	2.39168i
$325$	6.99648	+	16.8910i	0.388095	+	0.936944i
$326$	−2.05700	+	5.58725i	−0.113927	+	0.309449i
$327$	−31.5557	+	31.5557i	−1.74503	+	1.74503i
$328$	16.9713	−	21.6170i	0.937084	−	1.19360i
$329$	−0.944599	−	0.944599i	−0.0520775	−	0.0520775i
$330$	−26.7294	+	12.3441i	−1.47140	+	0.679519i
$331$	11.3494	−	4.70109i	0.623822	−	0.258395i	−0.0483038	−	0.998833i	$-0.515382\pi$
$331$	11.3494	−	4.70109i	0.623822	−	0.258395i	0.672125	+	0.740437i	$0.265382\pi$
$332$	−4.14572	+	12.8174i	−0.227526	+	0.703449i
$333$	−25.2069	+	60.8548i	−1.38133	+	3.33482i
$334$	−2.29787	−	2.12128i	−0.125734	−	0.116071i
$335$			32.9313i			1.79923i
$336$	−10.8911	+	6.71416i	−0.594157	+	0.366287i
$337$			13.6624i			0.744238i	0.928185	+	0.372119i	$0.121369\pi$
$337$			13.6624i			0.744238i	−0.928185	+	0.372119i	$0.878631\pi$
$338$	−0.240951	+	0.261009i	−0.0131060	+	0.0141970i
$339$	−5.54572	+	13.3886i	−0.301202	+	0.727167i
$340$	−6.72814	+	3.43949i	−0.364885	+	0.186533i
$341$	3.45505	−	1.43113i	0.187101	−	0.0774999i
$342$	22.2877	+	48.2609i	1.20518	+	2.60965i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	3.56756	+	6.34049i	0.192350	+	0.341856i
$345$	48.3801	−	48.3801i	2.60470	−	2.60470i
$346$	9.55111	+	3.51634i	0.513471	+	0.189040i
$347$	−2.14111	−	5.16911i	−0.114941	−	0.277492i	0.855931	−	0.517089i	$-0.172985\pi$
$347$	−2.14111	−	5.16911i	−0.114941	−	0.277492i	−0.970872	+	0.239597i	$0.922985\pi$
$348$	−8.53652	−	7.27117i	−0.457605	−	0.389776i
$349$	12.4196	+	5.14435i	0.664804	+	0.275371i	0.689459	−	0.724325i	$-0.257849\pi$
$349$	12.4196	+	5.14435i	0.664804	+	0.275371i	−0.0246543	+	0.999696i	$0.507849\pi$
$350$	7.09711	−	0.283595i	0.379356	−	0.0151588i
$351$	−49.2634			−2.62949
$352$	6.49361	+	9.64845i	0.346111	+	0.514264i
$353$	−0.915410			−0.0487224			−0.0243612	−	0.999703i	$-0.507755\pi$
$353$	−0.915410			−0.0487224			−0.0243612	+	0.999703i	$0.507755\pi$
$354$	−37.0555	+	1.48071i	−1.96948	+	0.0786989i
$355$	−25.9285	−	10.7399i	−1.37614	−	0.570017i
$356$	16.2926	−	19.1278i	0.863504	−	1.01377i
$357$	−1.46080	−	3.52669i	−0.0773140	−	0.186652i
$358$	−25.0233	−	9.21259i	−1.32252	−	0.486900i
$359$	−8.78552	+	8.78552i	−0.463682	+	0.463682i	−0.899860	−	0.436178i	$-0.856332\pi$
$359$	−8.78552	+	8.78552i	−0.463682	+	0.463682i	0.436178	+	0.899860i	$0.356332\pi$
$360$	62.3523	+	17.4503i	3.28625	+	0.919713i
$361$	−5.67290	−	5.67290i	−0.298573	−	0.298573i
$362$	10.0212	+	21.6996i	0.526704	+	1.14050i
$363$	20.0154	−	8.29064i	1.05053	−	0.435146i
$364$	3.31391	+	6.48249i	0.173696	+	0.339775i
$365$	0.747201	−	1.80390i	0.0391103	−	0.0944206i
$366$	15.8416	−	17.1603i	0.828053	−	0.896984i
$367$		−	8.71688i		−	0.455018i	−0.973776	−	0.227509i	$-0.926942\pi$
$367$		−	8.71688i		−	0.455018i	0.973776	−	0.227509i	$-0.0730581\pi$
$368$	−21.9077	−	15.8276i	−1.14202	−	0.825069i
$369$		−	70.2613i		−	3.65766i
$370$	−29.9667	−	27.6638i	−1.55790	−	1.43818i
$371$	−2.17988	+	5.26270i	−0.113174	+	0.273226i
$372$	−11.0716	−	3.58105i	−0.574038	−	0.185669i
$373$	−26.7498	+	11.0801i	−1.38505	+	0.573708i	−0.945828	−	0.324669i	$-0.894747\pi$
$373$	−26.7498	+	11.0801i	−1.38505	+	0.573708i	−0.439226	+	0.898377i	$0.644747\pi$
$374$	−3.15020	+	1.45482i	−0.162893	+	0.0752268i
$375$	−0.160514	−	0.160514i	−0.00828892	−	0.00828892i
$376$	3.75131	−	0.451623i	0.193459	−	0.0232907i
$377$	−4.51195	+	4.51195i	−0.232377	+	0.232377i
$378$	−6.61223	+	17.9602i	−0.340097	+	0.923772i
$379$	5.59606	+	13.5101i	0.287450	+	0.693966i	0.999970	−	0.00768545i	$-0.00244638\pi$
$379$	5.59606	+	13.5101i	0.287450	+	0.693966i	−0.712520	+	0.701651i	$0.752446\pi$
$380$	−32.8090	+	2.62624i	−1.68307	+	0.134723i
$381$	3.30146	+	1.36751i	0.169139	+	0.0700597i
$382$	−0.0574599	−	1.43796i	−0.00293990	−	0.0735725i
$383$	21.4950			1.09834			0.549171	−	0.835710i	$-0.314944\pi$
$383$	21.4950			1.09834			0.549171	+	0.835710i	$0.314944\pi$
$384$	4.08532	−	35.9565i	0.208478	−	1.83490i
$385$	6.50872			0.331715
$386$	−0.421338	−	10.5442i	−0.0214455	−	0.536685i
$387$	17.1836	+	7.11769i	0.873492	+	0.361812i
$388$	10.1613	−	0.813375i	0.515862	−	0.0412929i
$389$	−1.72385	−	4.16174i	−0.0874026	−	0.211009i	0.874134	−	0.485684i	$-0.161430\pi$
$389$	−1.72385	−	4.16174i	−0.0874026	−	0.211009i	−0.961537	+	0.274676i	$0.911430\pi$
$390$	18.0104	−	48.9198i	0.911990	−	2.47715i
$391$	5.70186	−	5.70186i	0.288356	−	0.288356i
$392$	2.80815	−	0.338075i	0.141833	−	0.0170754i
$393$	35.0616	+	35.0616i	1.76862	+	1.76862i
$394$	−0.982714	+	0.453834i	−0.0495084	+	0.0228638i
$395$	14.0204	−	5.80745i	0.705444	−	0.292204i
$396$	28.2898	+	9.15013i	1.42161	+	0.459811i
$397$	4.46228	−	10.7729i	0.223955	−	0.540676i	−0.771465	−	0.636272i	$-0.780476\pi$
$397$	4.46228	−	10.7729i	0.223955	−	0.540676i	0.995420	+	0.0955960i	$0.0304757\pi$
$398$	−6.54250	−	6.03972i	−0.327946	−	0.302744i
$399$		−	16.6273i		−	0.832408i
$400$	−11.7649	+	16.2844i	−0.588247	+	0.814219i
$401$			19.4844i			0.973006i	0.873679	+	0.486503i	$0.161728\pi$
$401$			19.4844i			0.973006i	−0.873679	+	0.486503i	$0.838272\pi$
$402$	31.9172	−	34.5741i	1.59188	−	1.72440i
$403$	−2.53394	+	6.11748i	−0.126225	+	0.304733i
$404$	3.27585	+	6.40804i	0.162980	+	0.318812i
$405$	63.1587	−	26.1612i	3.13838	−	1.29996i
$406$	1.03934	+	2.25054i	0.0515815	+	0.111693i
$407$	−13.2427	−	13.2427i	−0.656417	−	0.656417i
$408$	10.3973	+	2.90987i	0.514745	+	0.144060i
$409$	16.8705	−	16.8705i	0.834195	−	0.834195i	−0.153893	−	0.988088i	$-0.549181\pi$
$409$	16.8705	−	16.8705i	0.834195	−	0.834195i	0.988088	+	0.153893i	$0.0491810\pi$
$410$	40.8244	+	15.0299i	2.01617	+	0.742276i
$411$	23.4871	+	56.7029i	1.15853	+	2.79695i
$412$	−17.1759	+	20.1649i	−0.846196	+	0.993453i
$413$	7.57428	+	3.13737i	0.372706	+	0.154380i
$414$	−69.0402	+	2.75880i	−3.39314	+	0.135587i
$415$	−21.3237			−1.04674
$416$	−20.2098	−	3.94985i	−0.990868	−	0.193657i
$417$	33.2539			1.62845
$418$	−15.1023	+	0.603475i	−0.738675	+	0.0295169i
$419$	12.7338	+	5.27449i	0.622084	+	0.257676i	0.671386	−	0.741108i	$-0.265699\pi$
$419$	12.7338	+	5.27449i	0.622084	+	0.257676i	−0.0493012	+	0.998784i	$0.515699\pi$
$420$	−15.4175	−	13.1322i	−0.752299	−	0.640787i
$421$	6.37645	+	15.3941i	0.310769	+	0.750264i	0.999677	+	0.0254144i	$0.00809053\pi$
$421$	6.37645	+	15.3941i	0.310769	+	0.750264i	−0.688908	+	0.724849i	$0.741909\pi$
$422$	−27.8149	−	10.2403i	−1.35401	−	0.498492i
$423$	6.83036	−	6.83036i	0.332104	−	0.332104i
$424$	−7.90062	−	14.0415i	−0.383688	−	0.681914i
$425$	−4.23830	−	4.23830i	−0.205588	−	0.205588i
$426$	16.8128	+	36.4057i	0.814581	+	1.76386i
$427$	−4.76993	+	1.97577i	−0.230833	+	0.0956143i
$428$	−27.9900	+	14.3088i	−1.35295	+	0.691641i
$429$	9.16082	−	22.1162i	0.442288	−	1.06778i
$430$	−7.81147	+	8.46173i	−0.376702	+	0.408061i
$431$		−	17.0589i		−	0.821698i	−0.911703	−	0.410849i	$-0.865232\pi$
$431$		−	17.0589i		−	0.821698i	0.911703	−	0.410849i	$-0.134768\pi$
$432$	−28.4073	−	46.0797i	−1.36675	−	2.21701i
$433$		−	15.3127i		−	0.735883i	−0.929849	−	0.367941i	$-0.880063\pi$
$433$		−	15.3127i		−	0.735883i	0.929849	−	0.367941i	$-0.119937\pi$
$434$	1.89016	+	1.74491i	0.0907308	+	0.0837583i
$435$	6.79260	−	16.3988i	0.325680	−	0.786262i
$436$	−8.58729	+	26.5496i	−0.411257	+	1.27150i
$437$	32.4502	−	13.4413i	1.55230	−	0.642985i
$438$	−2.53282	+	1.16970i	−0.121023	+	0.0558905i
$439$	7.80636	+	7.80636i	0.372577	+	0.372577i	0.868415	−	0.495838i	$-0.165139\pi$
$439$	7.80636	+	7.80636i	0.372577	+	0.372577i	−0.495838	+	0.868415i	$0.665139\pi$
$440$	−11.3682	+	14.4800i	−0.541956	+	0.690309i
$441$	5.11306	−	5.11306i	0.243479	−	0.243479i
$442$	2.12262	−	5.76547i	0.100963	−	0.274235i
$443$	−11.7832	−	28.4471i	−0.559836	−	1.35156i	−0.909896	−	0.414837i	$-0.863839\pi$
$443$	−11.7832	−	28.4471i	−0.559836	−	1.35156i	0.350060	−	0.936727i	$-0.386161\pi$
$444$	4.64971	+	58.0877i	0.220665	+	2.75672i
$445$	36.7449	+	15.2202i	1.74187	+	0.721508i
$446$	0.0796935	+	1.99437i	0.00377360	+	0.0944362i
$447$	−37.3493			−1.76656
$448$	−4.15261	+	6.83782i	−0.196192	+	0.323057i
$449$	21.6243			1.02051			0.510257	−	0.860022i	$-0.329550\pi$
$449$	21.6243			1.02051			0.510257	+	0.860022i	$0.329550\pi$
$450$	2.05067	+	51.3189i	0.0966693	+	2.41920i
$451$	18.4563	+	7.64485i	0.869073	+	0.359982i
$452$	0.723011	+	9.03241i	0.0340076	+	0.424849i
$453$	9.38884	+	22.6667i	0.441126	+	1.06497i
$454$	−3.00761	+	8.16928i	−0.141154	+	0.383403i
$455$	−8.14889	+	8.14889i	−0.382026	+	0.382026i
$456$	36.9911	+	29.0414i	1.73227	+	1.35999i
$457$	−28.1055	−	28.1055i	−1.31472	−	1.31472i	−0.917894	−	0.396826i	$-0.870111\pi$
$457$	−28.1055	−	28.1055i	−1.31472	−	1.31472i	−0.396826	−	0.917894i	$-0.629889\pi$
$458$	−20.6548	+	9.53872i	−0.965135	+	0.445715i
$459$	14.9213	−	6.18061i	0.696467	−	0.288486i
$460$	13.1658	−	40.7051i	0.613857	−	1.89788i
$461$	13.8356	−	33.4021i	0.644388	−	1.55569i	−0.176315	−	0.984334i	$-0.556418\pi$
$461$	13.8356	−	33.4021i	0.644388	−	1.55569i	0.820703	−	0.571355i	$-0.193582\pi$
$462$	−6.83340	−	6.30827i	−0.317919	−	0.293487i
$463$		−	29.2753i		−	1.36054i	−0.732963	−	0.680268i	$-0.761863\pi$
$463$		−	29.2753i		−	1.36054i	0.732963	−	0.680268i	$-0.238137\pi$
$464$	−6.82214	−	1.61858i	−0.316710	−	0.0751407i
$465$		−	18.4193i		−	0.854177i
$466$	−20.8698	+	22.6071i	−0.966776	+	1.04725i
$467$	−6.74320	+	16.2795i	−0.312038	+	0.753326i	0.687591	+	0.726098i	$0.258668\pi$
$467$	−6.74320	+	16.2795i	−0.312038	+	0.753326i	−0.999629	+	0.0272282i	$0.991332\pi$
$468$	−46.8747	+	23.9628i	−2.16678	+	1.10768i
$469$	−9.61034	+	3.98073i	−0.443764	+	0.183813i
$470$	2.50758	+	5.42981i	0.115666	+	0.250458i
$471$	−12.2283	−	12.2283i	−0.563450	−	0.563450i
$472$	−20.2091	+	11.3709i	−0.930197	+	0.523387i
$473$	−3.73936	+	3.73936i	−0.171936	+	0.171936i
$474$	−20.3484	−	7.49149i	−0.934634	−	0.344096i
$475$	−9.99118	−	24.1208i	−0.458427	−	1.10674i
$476$	−1.81704	−	1.54770i	−0.0832839	−	0.0709389i
$477$	−38.0544	−	15.7626i	−1.74239	−	0.721721i
$478$	19.5993	−	0.783172i	0.896450	−	0.0358215i
$479$	−8.12573			−0.371274			−0.185637	−	0.982618i	$-0.559435\pi$
$479$	−8.12573			−0.371274			−0.185637	+	0.982618i	$0.559435\pi$
$480$	56.1439	−	11.3628i	2.56261	−	0.518639i
$481$	33.1597			1.51195
$482$	16.4450	−	0.657131i	0.749050	−	0.0299315i
$483$	19.9669	+	8.27057i	0.908527	+	0.376324i
$484$	8.78383	−	10.3124i	0.399265	−	0.468746i
$485$	6.17493	+	14.9076i	0.280389	+	0.676920i
$486$	−37.7844	−	13.9107i	−1.71393	−	0.631003i
$487$	5.14823	−	5.14823i	0.233289	−	0.233289i	−0.580775	−	0.814064i	$-0.697250\pi$
$487$	5.14823	−	5.14823i	0.233289	−	0.233289i	0.814064	+	0.580775i	$0.197250\pi$
$488$	3.93567	−	14.0626i	0.178159	−	0.636586i
$489$	9.52199	+	9.52199i	0.430599	+	0.430599i
$490$	1.87712	+	4.06464i	0.0847995	+	0.183622i
$491$	−26.5496	+	10.9972i	−1.19817	+	0.496297i	−0.890406	−	0.455167i	$-0.849579\pi$
$491$	−26.5496	+	10.9972i	−1.19817	+	0.496297i	−0.307760	+	0.951464i	$0.599579\pi$
$492$	−28.2939	−	55.3469i	−1.27559	−	2.49523i
$493$	0.800545	−	1.93269i	0.0360547	−	0.0870438i
$494$	18.1524	−	19.6635i	0.816716	−	0.884704i
$495$			47.0643i			2.11538i
$496$	−7.18330	+	1.15741i	−0.322540	+	0.0519692i
$497$		−	8.86494i		−	0.397647i
$498$	22.3875	+	20.6671i	1.00321	+	0.926113i
$499$	−5.41266	+	13.0673i	−0.242304	+	0.584973i	−0.997511	−	0.0705132i	$-0.977536\pi$
$499$	−5.41266	+	13.0673i	−0.242304	+	0.584973i	0.755207	+	0.655486i	$0.227536\pi$
$500$	−0.135050	−	0.0436810i	−0.00603962	−	0.00195347i
$501$	−6.53475	+	2.70678i	−0.291951	+	0.120930i
$502$	32.8111	−	15.1527i	1.46443	−	0.676298i
$503$	−23.4449	−	23.4449i	−1.04535	−	1.04535i	−0.998921	−	0.0464328i	$-0.985215\pi$
$503$	−23.4449	−	23.4449i	−1.04535	−	1.04535i	−0.0464328	−	0.998921i	$-0.514785\pi$
$504$	2.44461	+	20.3056i	0.108891	+	0.904484i
$505$	−8.05530	+	8.05530i	−0.358456	+	0.358456i
$506$	6.78731	−	18.4357i	0.301733	−	0.819568i
$507$	0.307456	+	0.742265i	0.0136546	+	0.0329652i
$508$	2.22729	−	0.178286i	0.0988198	−	0.00791016i
$509$	38.9017	+	16.1136i	1.72429	+	0.714222i	0.999686	+	0.0250523i	$0.00797521\pi$
$509$	38.9017	+	16.1136i	1.72429	+	0.714222i	0.724599	+	0.689170i	$0.242025\pi$
$510$	0.682377	+	17.0768i	0.0302162	+	0.756174i
$511$	0.616753			0.0272836
$512$	−7.95924	−	21.1814i	−0.351752	−	0.936093i
$513$	70.3496			3.10601
$514$	−0.161020	−	4.02959i	−0.00710227	−	0.177738i
$515$	−38.7371	−	16.0454i	−1.70696	−	0.707046i
$516$	16.4023	−	1.31294i	0.722070	−	0.0577991i
$517$	1.05102	+	2.53739i	0.0462238	+	0.111594i
$518$	4.45076	−	12.0892i	0.195555	−	0.531168i
$519$	16.2774	−	16.2774i	0.714497	−	0.714497i
$520$	−3.89607	−	32.3619i	−0.170854	−	1.41916i
$521$	−17.8120	−	17.8120i	−0.780359	−	0.780359i	0.199532	−	0.979891i	$-0.436058\pi$
$521$	−17.8120	−	17.8120i	−0.780359	−	0.780359i	−0.979891	+	0.199532i	$0.936058\pi$
$522$	−16.2736	+	7.51542i	−0.712276	+	0.328941i
$523$	−4.78851	+	1.98347i	−0.209387	+	0.0867309i	−0.484912	−	0.874563i	$-0.661148\pi$
$523$	−4.78851	+	1.98347i	−0.209387	+	0.0867309i	0.275525	+	0.961294i	$0.411148\pi$
$524$	29.4993	+	9.54136i	1.28868	+	0.416816i
$525$	6.14767	−	14.8418i	0.268306	−	0.647749i
$526$	14.0541	+	12.9741i	0.612789	+	0.565698i
$527$		−	2.17082i		−	0.0945624i
$528$	25.9694	−	4.18432i	1.13017	−	0.182099i
$529$			22.6536i			0.984940i
$530$	17.2991	−	18.7391i	0.751423	−	0.813975i
$531$	−22.6862	+	54.7694i	−0.984498	+	2.37679i
$532$	−4.73236	−	9.25719i	−0.205174	−	0.401350i
$533$	−32.6786	+	13.5359i	−1.41547	+	0.586305i
$534$	−23.8264	−	51.5928i	−1.03107	−	2.23264i
$535$	−35.1852	−	35.1852i	−1.52119	−	1.52119i
$536$	7.92948	−	28.3330i	0.342501	−	1.22380i
$537$	−42.6456	+	42.6456i	−1.84029	+	1.84029i
$538$	−7.89306	−	2.90591i	−0.340294	−	0.125283i
$539$	0.786772	+	1.89943i	0.0338887	+	0.0818144i
$540$	55.5620	−	65.2310i	2.39101	−	2.80710i
$541$	13.3988	+	5.54995i	0.576058	+	0.238611i	0.651640	−	0.758528i	$-0.274081\pi$
$541$	13.3988	+	5.54995i	0.576058	+	0.238611i	−0.0755816	+	0.997140i	$0.524081\pi$
$542$	−19.2215	+	0.768075i	−0.825632	+	0.0329916i
$543$	54.0597			2.31992
$544$	6.61686	−	1.33917i	0.283696	−	0.0574164i
$545$	−44.1693			−1.89200
$546$	16.4533	−	0.657463i	0.704138	−	0.0281368i
$547$	24.4429	+	10.1246i	1.04510	+	0.432895i	0.838141	−	0.545454i	$-0.183643\pi$
$547$	24.4429	+	10.1246i	1.04510	+	0.432895i	0.206961	+	0.978349i	$0.433643\pi$
$548$	29.2148	+	24.8843i	1.24799	+	1.06301i
$549$	−14.2867	−	34.4912i	−0.609743	−	1.47205i
$550$	−13.7036	−	5.04513i	−0.584324	−	0.215125i
$551$	6.44320	−	6.44320i	0.274489	−	0.274489i
$552$	−53.2740	+	29.9753i	−2.26749	+	1.27583i
$553$	3.38957	+	3.38957i	0.144139	+	0.144139i
$554$	−11.0859	−	24.0049i	−0.470993	−	1.01987i
$555$	−85.2203	+	35.2994i	−3.61740	+	1.49838i
$556$	18.5139	−	9.46450i	0.785165	−	0.401384i
$557$	−2.31825	+	5.59675i	−0.0982275	+	0.237142i	−0.965353	−	0.260948i	$-0.915965\pi$
$557$	−2.31825	+	5.59675i	−0.0982275	+	0.237142i	0.867125	+	0.498090i	$0.165965\pi$
$558$	−12.6174	+	13.6677i	−0.534136	+	0.578600i
$559$		−	9.36333i		−	0.396027i
$560$	−12.3212	−	2.92327i	−0.520668	−	0.123531i
$561$			7.84804i			0.331345i
$562$	−1.02041	−	0.941992i	−0.0430433	−	0.0397356i
$563$	7.10218	−	17.1462i	0.299321	−	0.722625i	−0.700637	−	0.713517i	$-0.747101\pi$
$563$	7.10218	−	17.1462i	0.299321	−	0.722625i	0.999959	−	0.00910755i	$-0.00289906\pi$
$564$	2.62992	−	8.13103i	0.110740	−	0.342378i
$565$	−13.2514	+	5.48891i	−0.557491	+	0.230920i
$566$	−27.0191	+	12.4779i	−1.13570	+	0.524484i
$567$	15.2692	+	15.2692i	0.641247	+	0.641247i
$568$	19.7220	+	15.4836i	0.827516	+	0.649676i
$569$	−30.1597	+	30.1597i	−1.26436	+	1.26436i	−0.315401	+	0.948959i	$0.602139\pi$
$569$	−30.1597	+	30.1597i	−1.26436	+	1.26436i	−0.948959	+	0.315401i	$0.897861\pi$
$570$	−25.7193	+	69.8590i	−1.07726	+	2.92607i
$571$	10.2648	+	24.7815i	0.429570	+	1.03707i	0.979424	+	0.201814i	$0.0646835\pi$
$571$	10.2648	+	24.7815i	0.429570	+	1.03707i	−0.549854	+	0.835261i	$0.685316\pi$
$572$	−1.19432	−	14.9204i	−0.0499370	−	0.623852i
$573$	−3.00713	−	1.24559i	−0.125625	−	0.0520355i
$574$	0.548664	+	13.7306i	0.0229008	+	0.573103i
$575$	33.9352			1.41520
$576$	−49.4440	−	30.0274i	−2.06017	−	1.25114i
$577$	18.4431			0.767796			0.383898	−	0.923376i	$-0.374581\pi$
$577$	18.4431			0.767796			0.383898	+	0.923376i	$0.374581\pi$
$578$	−0.879498	−	22.0099i	−0.0365823	−	0.915490i
$579$	−22.0505	−	9.13361i	−0.916387	−	0.379580i
$580$	−0.885570	−	11.0632i	−0.0367713	−	0.459375i
$581$	−2.57761	−	6.22290i	−0.106937	−	0.258169i
$582$	7.96554	−	21.6360i	0.330182	−	0.896843i
$583$	8.28108	−	8.28108i	0.342967	−	0.342967i
$584$	−1.07723	+	1.37210i	−0.0445759	+	0.0567780i
$585$	−58.9243	−	58.9243i	−2.43622	−	2.43622i
$586$	32.3099	−	14.9212i	1.33471	−	0.616390i
$587$	3.96843	−	1.64378i	0.163795	−	0.0678460i	−0.299280	−	0.954165i	$-0.596746\pi$
$587$	3.96843	−	1.64378i	0.163795	−	0.0678460i	0.463074	+	0.886319i	$0.346746\pi$
$588$	1.96870	−	6.08671i	0.0811880	−	0.251012i
$589$	3.61854	−	8.73593i	0.149099	−	0.359958i
$590$	−26.9701	−	24.8975i	−1.11034	−	1.02501i
$591$			2.44822i			0.100706i
$592$	19.1213	+	31.0167i	0.785879	+	1.27478i
$593$			9.51410i			0.390697i	0.980734	+	0.195349i	$0.0625838\pi$
$593$			9.51410i			0.390697i	−0.980734	+	0.195349i	$0.937416\pi$
$594$	26.6901	−	28.9119i	1.09511	−	1.18627i
$595$	1.44584	−	3.49056i	0.0592736	−	0.143099i
$596$	−20.7940	+	10.6301i	−0.851757	+	0.435426i
$597$	−18.6058	+	7.70676i	−0.761483	+	0.315417i
$598$	14.5838	+	31.5791i	0.596375	+	1.29137i
$599$	−3.24666	−	3.24666i	−0.132655	−	0.132655i	0.637662	−	0.770317i	$-0.279902\pi$
$599$	−3.24666	−	3.24666i	−0.132655	−	0.132655i	−0.770317	+	0.637662i	$0.779902\pi$
$600$	22.2812	+	39.5996i	0.909627	+	1.61665i
$601$	−0.490989	+	0.490989i	−0.0200279	+	0.0200279i	−0.717050	−	0.697022i	$-0.754508\pi$
$601$	−0.490989	+	0.490989i	−0.0200279	+	0.0200279i	0.697022	+	0.717050i	$0.254508\pi$
$602$	−3.41363	−	1.25676i	−0.139129	−	0.0512219i
$603$	−28.7845	−	69.4920i	−1.17220	−	2.82993i
$604$	11.6784	+	9.94736i	0.475188	+	0.404752i
$605$	19.8103	+	8.20570i	0.805404	+	0.333609i
$606$	16.2644	−	0.649912i	0.660695	−	0.0264009i
$607$	−44.6088			−1.81061			−0.905307	−	0.424758i	$-0.860359\pi$
$607$	−44.6088			−1.81061			−0.905307	+	0.424758i	$0.860359\pi$
$608$	28.8602	+	5.64049i	1.17044	+	0.228752i
$609$	5.60674			0.227196
$610$	23.0968	−	0.922931i	0.935162	−	0.0373684i
$611$	−4.49268	−	1.86093i	−0.181754	−	0.0752851i
$612$	11.1914	−	13.1389i	0.452385	−	0.531111i
$613$	−8.54332	−	20.6254i	−0.345061	−	0.833052i	−0.997188	−	0.0749416i	$-0.976123\pi$
$613$	−8.54332	−	20.6254i	−0.345061	−	0.833052i	0.652127	−	0.758110i	$-0.273877\pi$
$614$	26.1917	+	9.64275i	1.05701	+	0.389150i
$615$	69.5744	−	69.5744i	2.80551	−	2.80551i
$616$	−5.59989	−	1.56722i	−0.225626	−	0.0631451i
$617$	−14.4545	−	14.4545i	−0.581917	−	0.581917i	0.353513	−	0.935430i	$-0.384987\pi$
$617$	−14.4545	−	14.4545i	−0.581917	−	0.581917i	−0.935430	+	0.353513i	$0.884987\pi$
$618$	25.1182	+	54.3900i	1.01040	+	2.18789i
$619$	17.8843	−	7.40793i	0.718832	−	0.297750i	0.00687810	−	0.999976i	$-0.497811\pi$
$619$	17.8843	−	7.40793i	0.718832	−	0.297750i	0.711954	+	0.702227i	$0.247811\pi$
$620$	−5.24239	−	10.2549i	−0.210540	−	0.411846i
$621$	−34.9925	+	84.4793i	−1.40420	+	3.39004i
$622$	25.1567	−	27.2508i	1.00869	−	1.09266i
$623$			12.5631i			0.503328i
$624$	−27.2748	+	37.7524i	−1.09187	+	1.51130i
$625$			24.8874i			0.995496i
$626$	−31.2211	−	28.8218i	−1.24785	−	1.15195i
$627$	−13.0819	+	31.5825i	−0.522441	+	1.26128i
$628$	−10.2884	−	3.32770i	−0.410551	−	0.132790i
$629$	−10.0437	+	4.16023i	−0.400467	+	0.165879i
$630$	−29.3912	+	13.5734i	−1.17097	+	0.540776i
$631$	−16.9371	−	16.9371i	−0.674257	−	0.674257i	0.284438	−	0.958695i	$-0.408193\pi$
$631$	−16.9371	−	16.9371i	−0.674257	−	0.674257i	−0.958695	+	0.284438i	$0.908193\pi$
$632$	−13.4611	+	1.62059i	−0.535453	+	0.0644635i
$633$	−47.4031	+	47.4031i	−1.88410	+	1.88410i
$634$	−7.26705	+	19.7388i	−0.288611	+	0.783928i
$635$	1.35350	+	3.26764i	0.0537121	+	0.129672i
$636$	−36.3241	+	2.90761i	−1.44034	+	0.115294i
$637$	−3.36312	−	1.39305i	−0.133252	−	0.0551947i
$638$	−0.203492	−	5.09248i	−0.00805632	−	0.201613i
$639$	64.1021			2.53584
$640$	28.0238	−	22.3055i	1.10774	−	0.881702i
$641$	−19.5093			−0.770570			−0.385285	−	0.922798i	$-0.625897\pi$
$641$	−19.5093			−0.770570			−0.385285	+	0.922798i	$0.625897\pi$
$642$	2.83879	+	71.0420i	0.112038	+	2.80381i
$643$	−32.2084	−	13.3412i	−1.27018	−	0.526124i	−0.357158	−	0.934044i	$-0.616254\pi$
$643$	−32.2084	−	13.3412i	−1.27018	−	0.526124i	−0.913018	+	0.407920i	$0.866254\pi$
$644$	13.4704	−	1.07826i	0.530808	−	0.0424893i
$645$	9.96752	+	24.0637i	0.392471	+	0.947508i
$646$	−3.03116	+	8.23326i	−0.119259	+	0.323933i
$647$	2.60134	−	2.60134i	0.102269	−	0.102269i	−0.654121	−	0.756390i	$-0.726961\pi$
$647$	2.60134	−	2.60134i	0.102269	−	0.102269i	0.756390	+	0.654121i	$0.226961\pi$
$648$	−60.6390	+	7.30037i	−2.38212	+	0.286785i
$649$	−11.9185	−	11.9185i	−0.467841	−	0.467841i
$650$	23.4734	−	10.8404i	0.920701	−	0.425195i
$651$	5.37531	−	2.22652i	0.210675	−	0.0872644i
$652$	8.01141	+	2.59123i	0.313751	+	0.101481i
$653$	15.3075	−	36.9555i	0.599028	−	1.44618i	−0.275546	−	0.961288i	$-0.588859\pi$
$653$	15.3075	−	36.9555i	0.599028	−	1.44618i	0.874574	−	0.484893i	$-0.161141\pi$
$654$	46.3727	+	42.8090i	1.81331	+	1.67397i
$655$			49.0766i			1.91758i
$656$	−31.5049	−	22.7613i	−1.23006	−	0.888679i
$657$			4.45972i			0.173990i
$658$	−1.28146	+	1.38814i	−0.0499566	+	0.0541152i
$659$	5.71860	−	13.8059i	0.222765	−	0.537802i	−0.772498	−	0.635017i	$-0.780993\pi$
$659$	5.71860	−	13.8059i	0.222765	−	0.537802i	0.995263	+	0.0972143i	$0.0309932\pi$
$660$	18.9525	+	37.0739i	0.737726	+	1.44310i
$661$	33.7756	−	13.9903i	1.31372	−	0.544160i	0.387752	−	0.921764i	$-0.373252\pi$
$661$	33.7756	−	13.9903i	1.31372	−	0.544160i	0.925967	+	0.377603i	$0.123252\pi$
$662$	−7.28390	−	15.7723i	−0.283097	−	0.613007i
$663$	−9.82573	−	9.82573i	−0.381600	−	0.381600i
$664$	18.3462	+	5.13450i	0.711973	+	0.199257i
$665$	11.6369	−	11.6369i	0.451258	−	0.451258i
$666$	87.4163	+	32.1833i	3.38731	+	1.24708i
$667$	4.53241	+	10.9422i	0.175496	+	0.423684i
$668$	−2.86780	+	3.36687i	−0.110959	+	0.130268i
$669$	4.17072	+	1.72757i	0.161249	+	0.0667916i
$670$	46.5348	−	1.85950i	1.79780	−	0.0718386i
$671$	10.6147			0.409774
$672$	10.1027	+	15.0109i	0.389718	+	0.579058i
$673$	11.9429			0.460366			0.230183	−	0.973147i	$-0.426067\pi$
$673$	11.9429			0.460366			0.230183	+	0.973147i	$0.426067\pi$
$674$	19.3061	−	0.771459i	0.743645	−	0.0297155i
$675$	62.7951	+	26.0106i	2.41698	+	1.00115i
$676$	0.382434	+	0.325746i	0.0147090	+	0.0125287i
$677$	−3.20627	−	7.74061i	−0.123227	−	0.297496i	0.850213	−	0.526439i	$-0.176473\pi$
$677$	−3.20627	−	7.74061i	−0.123227	−	0.297496i	−0.973440	+	0.228943i	$0.926473\pi$
$678$	19.2323	+	7.08059i	0.738613	+	0.271928i
$679$	−3.60405	+	3.60405i	−0.138311	+	0.138311i
$680$	5.24021	+	9.31323i	0.200953	+	0.357146i
$681$	13.9224	+	13.9224i	0.533507	+	0.533507i
$682$	−2.21740	−	4.80147i	−0.0849086	−	0.183858i
$683$	1.82826	−	0.757291i	0.0699565	−	0.0289769i	−0.347431	−	0.937706i	$-0.612946\pi$
$683$	1.82826	−	0.757291i	0.0699565	−	0.0289769i	0.417387	+	0.908729i	$0.362946\pi$
$684$	66.9384	−	34.2195i	2.55945	−	1.30842i
$685$	−23.2465	+	56.1220i	−0.888203	+	2.14431i
$686$	−0.959275	+	1.03913i	−0.0366253	+	0.0396742i
$687$			51.4569i			1.96320i
$688$	8.75821	−	5.39929i	0.333904	−	0.205846i
$689$			20.7358i			0.789970i
$690$	−71.0971	−	65.6335i	−2.70662	−	2.49862i
$691$	−0.334627	+	0.807862i	−0.0127298	+	0.0307325i	−0.930117	−	0.367264i	$-0.880294\pi$
$691$	−0.334627	+	0.807862i	−0.0127298	+	0.0307325i	0.917387	+	0.397997i	$0.130294\pi$
$692$	4.42958	−	13.6951i	0.168388	−	0.520609i
$693$	−13.7347	+	5.68912i	−0.521740	+	0.216112i
$694$	−7.18349	+	3.31746i	−0.272682	+	0.125929i
$695$	23.2731	+	23.2731i	0.882800	+	0.882800i
$696$	−9.79277	+	12.4734i	−0.371194	+	0.472803i
$697$	8.19973	−	8.19973i	0.310587	−	0.310587i
$698$	6.56813	−	17.8404i	0.248607	−	0.675269i
$699$	26.6301	+	64.2908i	1.00724	+	2.43170i
$700$	−0.801488	−	10.0128i	−0.0302934	−	0.378449i
$701$	5.16656	+	2.14006i	0.195138	+	0.0808289i	0.478113	−	0.878299i	$-0.341321\pi$
$701$	5.16656	+	2.14006i	0.195138	+	0.0808289i	−0.282974	+	0.959128i	$0.591321\pi$
$702$	2.78170	+	69.6135i	0.104989	+	2.62739i
$703$	−47.3530			−1.78595
$704$	13.2674	−	9.72084i	0.500035	−	0.366368i
$705$	13.5272			0.509463
$706$	0.0516894	+	1.29355i	0.00194536	+	0.0486835i
$707$	−3.32450	−	1.37705i	−0.125031	−	0.0517893i
$708$	4.18474	+	52.2790i	0.157272	+	1.96477i
$709$	−14.3082	−	34.5431i	−0.537356	−	1.29729i	−0.926562	−	0.376142i	$-0.877251\pi$
$709$	−14.3082	−	34.5431i	−0.537356	−	1.29729i	0.389206	−	0.921151i	$-0.372749\pi$
$710$	−13.7124	+	37.2456i	−0.514617	+	1.39780i
$711$	−24.5098	+	24.5098i	−0.919191	+	0.919191i
$712$	−27.9492	−	21.9427i	−1.04744	−	0.822338i
$713$	8.69065	+	8.69065i	0.325467	+	0.325467i
$714$	−4.90103	+	2.26338i	−0.183417	+	0.0847048i
$715$	21.8896	−	9.06697i	0.818625	−	0.339085i
$716$	−11.6052	+	35.8802i	−0.433707	+	1.34091i
$717$	16.9773	−	40.9869i	0.634030	−	1.53068i
$718$	12.9108	+	11.9186i	0.481826	+	0.444799i
$719$			27.4373i			1.02324i	0.859212	+	0.511620i	$0.170954\pi$
$719$			27.4373i			1.02324i	−0.859212	+	0.511620i	$0.829046\pi$
$720$	21.1380	−	89.0945i	0.787768	−	3.32036i
$721$		−	13.2442i		−	0.493239i
$722$	−7.69596	+	8.33661i	−0.286414	+	0.310257i
$723$	14.2450	−	34.3906i	0.529779	−	1.27900i
$724$	30.0975	−	15.3861i	1.11856	−	0.571821i
$725$	8.13355	−	3.36903i	0.302072	−	0.125123i
$726$	−12.8456	−	27.8153i	−0.476744	−	1.03232i
$727$	−29.9948	−	29.9948i	−1.11245	−	1.11245i	−0.992819	−	0.119628i	$-0.961830\pi$
$727$	−29.9948	−	29.9948i	−1.11245	−	1.11245i	−0.119628	−	0.992819i	$-0.538170\pi$
$728$	8.97319	−	5.04888i	0.332569	−	0.187124i
$729$	−18.5859	+	18.5859i	−0.688366	+	0.688366i
$730$	−2.59126	−	0.954000i	−0.0959068	−	0.0353091i
$731$	1.17473	+	2.83604i	0.0434488	+	0.104895i
$732$	−25.1435	−	21.4165i	−0.929331	−	0.791578i
$733$	−44.3580	−	18.3737i	−1.63840	−	0.678647i	−0.642264	−	0.766483i	$-0.722005\pi$
$733$	−44.3580	−	18.3737i	−1.63840	−	0.678647i	−0.996135	+	0.0878362i	$0.972005\pi$
$734$	−12.3177	+	0.492206i	−0.454655	+	0.0181677i
$735$	10.1262			0.373509
$736$	−21.1287	+	31.8511i	−0.778814	+	1.17405i
$737$	21.3861			0.787768
$738$	−99.2853	+	3.96737i	−3.65474	+	0.146041i
$739$	−9.24889	−	3.83102i	−0.340226	−	0.140926i	0.206027	−	0.978546i	$-0.433946\pi$
$739$	−9.24889	−	3.83102i	−0.340226	−	0.140926i	−0.546253	+	0.837620i	$0.683946\pi$
$740$	−37.3993	+	43.9076i	−1.37483	+	1.61408i
$741$	−23.1627	−	55.9197i	−0.850904	−	2.05426i
$742$	7.55973	+	2.78320i	0.277526	+	0.102174i
$743$	−25.5282	+	25.5282i	−0.936539	+	0.936539i	−0.998103	−	0.0615643i	$-0.980391\pi$
$743$	−25.5282	+	25.5282i	−0.936539	+	0.936539i	0.0615643	+	0.998103i	$0.480391\pi$
$744$	−4.43516	+	15.8474i	−0.162601	+	0.580994i
$745$	−26.1394	−	26.1394i	−0.957673	−	0.957673i
$746$	17.1676	+	37.1742i	0.628552	+	1.36104i
$747$	44.9975	−	18.6386i	1.64637	−	0.681950i
$748$	2.23366	+	4.36936i	0.0816707	+	0.159760i
$749$	6.01490	−	14.5212i	0.219780	−	0.530595i
$750$	−0.217757	+	0.235884i	−0.00795136	+	0.00861327i
$751$		−	31.1220i		−	1.13566i	−0.823147	−	0.567828i	$-0.807784\pi$
$751$		−	31.1220i		−	1.13566i	0.823147	−	0.567828i	$-0.192216\pi$
$752$	−0.850002	−	5.27542i	−0.0309964	−	0.192375i
$753$		−	81.7416i		−	2.97883i
$754$	6.63054	+	6.12100i	0.241470	+	0.222914i
$755$	−9.29265	+	22.4345i	−0.338194	+	0.816473i
$756$	25.7526	+	8.32951i	0.936615	+	0.302942i
$757$	29.5271	−	12.2305i	1.07318	−	0.444526i	0.225068	−	0.974343i	$-0.427740\pi$
$757$	29.5271	−	12.2305i	1.07318	−	0.444526i	0.848112	+	0.529817i	$0.177740\pi$
$758$	18.7749	−	8.67057i	0.681935	−	0.314929i
$759$	−31.4188	−	31.4188i	−1.14043	−	1.14043i
$760$	5.56370	+	46.2137i	0.201817	+	1.67635i
$761$	−9.91036	+	9.91036i	−0.359250	+	0.359250i	−0.863537	−	0.504286i	$-0.831756\pi$
$761$	−9.91036	+	9.91036i	−0.359250	+	0.359250i	0.504286	+	0.863537i	$0.331756\pi$
$762$	1.74599	−	4.74247i	0.0632506	−	0.171802i
$763$	−5.33917	−	12.8899i	−0.193291	−	0.466646i
$764$	−2.02872	+	0.162391i	−0.0733965	+	0.00587512i
$765$	25.2401	+	10.4548i	0.912559	+	0.377994i
$766$	−1.21373	−	30.3742i	−0.0438539	−	1.09747i
$767$	29.8438			1.07760
$768$	−51.0404	−	3.74259i	−1.84176	−	0.135049i
$769$	51.0896			1.84234			0.921170	−	0.389162i	$-0.127235\pi$
$769$	51.0896			1.84234			0.921170	+	0.389162i	$0.127235\pi$
$770$	−0.367520	−	9.19737i	−0.0132445	−	0.331450i
$771$	−8.42687	−	3.49052i	−0.303486	−	0.125708i
$772$	−14.8760	+	1.19077i	−0.535401	+	0.0428568i
$773$	11.3351	+	27.3654i	0.407695	+	0.984263i	0.985743	+	0.168260i	$0.0538148\pi$
$773$	11.3351	+	27.3654i	0.407695	+	0.984263i	−0.578047	+	0.816003i	$0.696185\pi$
$774$	9.08761	−	24.6838i	0.326648	−	0.887242i
$775$	6.45992	−	6.45992i	0.232047	−	0.232047i
$776$	−1.72314	−	14.3129i	−0.0618569	−	0.513802i
$777$	−20.6028	−	20.6028i	−0.739122	−	0.739122i
$778$	−5.78356	+	2.67094i	−0.207351	+	0.0957579i
$779$	46.6659	−	19.3297i	1.67198	−	0.692557i
$780$	−70.1449	−	22.6879i	−2.51159	−	0.812357i
$781$	−6.97469	+	16.8384i	−0.249574	+	0.602525i
$782$	−8.37918	−	7.73526i	−0.299639	−	0.276612i
$783$			23.7219i			0.847751i
$784$	−0.636293	−	3.94907i	−0.0227248	−	0.141038i
$785$		−	17.1162i		−	0.610905i
$786$	47.5652	−	51.5248i	1.69659	−	1.83783i
$787$	−15.5768	+	37.6057i	−0.555253	+	1.34050i	0.358234	+	0.933632i	$0.383379\pi$
$787$	−15.5768	+	37.6057i	−0.555253	+	1.34050i	−0.913487	+	0.406868i	$0.866621\pi$
$788$	0.696796	+	1.36303i	0.0248223	+	0.0485560i
$789$	39.9676	−	16.5551i	1.42288	−	0.589377i
$790$	−8.99810	−	19.4841i	−0.320138	−	0.693214i
$791$	−3.20365	−	3.20365i	−0.113909	−	0.113909i
$792$	11.3325	−	40.4926i	0.402683	−	1.43884i
$793$	−13.2895	+	13.2895i	−0.471925	+	0.471925i
$794$	−15.4750	−	5.69728i	−0.549187	−	0.202189i
$795$	−22.0738	−	53.2909i	−0.782877	−	1.89003i
$796$	−8.16522	+	9.58615i	−0.289409	+	0.339772i
$797$	−3.24999	−	1.34619i	−0.115120	−	0.0476845i	0.324380	−	0.945927i	$-0.394844\pi$
$797$	−3.24999	−	1.34619i	−0.115120	−	0.0476845i	−0.439500	+	0.898242i	$0.644844\pi$
$798$	−23.4958	+	0.938876i	−0.831744	+	0.0332359i
$799$	1.59425			0.0564006
$800$	23.6755	+	15.7054i	0.837057	+	0.555268i
$801$	−90.8430			−3.20978
$802$	27.5332	−	1.10020i	0.972230	−	0.0388496i
$803$	−1.17148	−	0.485244i	−0.0413407	−	0.0171239i
$804$	−50.6585	−	43.1495i	−1.78659	−	1.52176i
$805$	8.18585	+	19.7624i	0.288513	+	0.696532i
$806$	8.78760	+	3.23525i	0.309530	+	0.113957i
$807$	−13.4516	+	13.4516i	−0.473520	+	0.473520i
$808$	8.87013	−	4.99089i	0.312050	−	0.175579i
$809$	26.2641	+	26.2641i	0.923395	+	0.923395i	0.997268	−	0.0738727i	$-0.0235359\pi$
$809$	26.2641	+	26.2641i	0.923395	+	0.923395i	−0.0738727	+	0.997268i	$0.523536\pi$
$810$	−40.5343	−	87.7715i	−1.42423	−	3.08397i
$811$	47.5491	−	19.6955i	1.66967	−	0.691601i	0.670920	−	0.741529i	$-0.265899\pi$
$811$	47.5491	−	19.6955i	1.66967	−	0.691601i	0.998753	+	0.0499281i	$0.0158992\pi$
$812$	3.12152	−	1.59575i	0.109544	−	0.0560000i
$813$	−16.6501	+	40.1968i	−0.583943	+	1.40976i
$814$	−17.9653	+	19.4609i	−0.629685	+	0.682103i
$815$			13.3282i			0.466866i
$816$	3.52480	−	14.8566i	0.123393	−	0.520087i
$817$			13.3711i			0.467796i
$818$	−24.7921	−	22.8869i	−0.866837	−	0.800222i
$819$	10.0731	−	24.3186i	0.351982	−	0.849761i
$820$	18.9334	−	58.5371i	0.661183	−	2.04420i
$821$	−12.5277	+	5.18913i	−0.437219	+	0.181102i	−0.590425	−	0.807092i	$-0.701040\pi$
$821$	−12.5277	+	5.18913i	−0.437219	+	0.181102i	0.153207	+	0.988194i	$0.451040\pi$
$822$	78.7999	−	36.3911i	2.74846	−	1.26928i
$823$	−5.94025	−	5.94025i	−0.207064	−	0.207064i	0.595954	−	0.803018i	$-0.296774\pi$
$823$	−5.94025	−	5.94025i	−0.207064	−	0.207064i	−0.803018	+	0.595954i	$0.796774\pi$
$824$	29.4646	+	23.1324i	1.02645	+	0.805855i
$825$	−23.3542	+	23.3542i	−0.813089	+	0.813089i
$826$	4.00569	−	10.8803i	0.139376	−	0.378573i
$827$	−2.73813	−	6.61042i	−0.0952140	−	0.229867i	0.869096	−	0.494644i	$-0.164702\pi$
$827$	−2.73813	−	6.61042i	−0.0952140	−	0.229867i	−0.964310	+	0.264777i	$0.914702\pi$
$828$	7.79683	+	97.4040i	0.270959	+	3.38502i
$829$	−23.6517	−	9.79687i	−0.821459	−	0.340259i	−0.0679429	−	0.997689i	$-0.521644\pi$
$829$	−23.6517	−	9.79687i	−0.821459	−	0.340259i	−0.753516	+	0.657430i	$0.771644\pi$
$830$	1.20406	+	30.1323i	0.0417936	+	1.04591i
$831$	−59.8030			−2.07454
$832$	−4.44031	+	28.7812i	−0.153940	+	0.997810i
$833$	1.19342			0.0413496
$834$	−1.87771	−	46.9905i	−0.0650197	−	1.62715i
$835$	−6.46781	−	2.67905i	−0.223828	−	0.0927124i
$836$	1.70552	+	21.3067i	0.0589868	+	0.736908i
$837$	9.42034	+	22.7427i	0.325615	+	0.786103i
$838$	6.73429	−	18.2917i	0.232632	−	0.631877i
$839$	9.57478	−	9.57478i	0.330558	−	0.330558i	−0.522240	−	0.852798i	$-0.674904\pi$
$839$	9.57478	−	9.57478i	0.330558	−	0.330558i	0.852798	+	0.522240i	$0.174904\pi$
$840$	−17.6864	+	22.5278i	−0.610239	+	0.777284i
$841$	−18.3335	−	18.3335i	−0.632188	−	0.632188i
$842$	21.3932	−	9.87972i	0.737257	−	0.340478i
$843$	−2.90187	+	1.20199i	−0.0999457	+	0.0413989i
$844$	−12.8999	+	39.8830i	−0.444032	+	1.37283i
$845$	−0.304307	+	0.734661i	−0.0104685	+	0.0252731i
$846$	−10.0376	−	9.26621i	−0.345099	−	0.318579i
$847$			6.77314i			0.232728i
$848$	−19.3957	+	11.9571i	−0.666051	+	0.410609i
$849$			67.3122i			2.31015i
$850$	−5.74977	+	6.22840i	−0.197215	+	0.213632i
$851$	23.5538	−	56.8638i	0.807413	−	1.94927i
$852$	50.4951	−	25.8136i	1.72993	−	0.884358i
$853$	4.52075	−	1.87256i	0.154788	−	0.0641151i	−0.303945	−	0.952690i	$-0.598304\pi$
$853$	4.52075	−	1.87256i	0.154788	−	0.0641151i	0.458732	+	0.888575i	$0.348304\pi$
$854$	3.06127	+	6.62876i	0.104755	+	0.226832i
$855$	84.1456	+	84.1456i	2.87772	+	2.87772i
$856$	21.8000	+	38.7444i	0.745109	+	1.32425i
$857$	26.4676	−	26.4676i	0.904117	−	0.904117i	−0.0916725	−	0.995789i	$-0.529221\pi$
$857$	26.4676	−	26.4676i	0.904117	−	0.904117i	0.995789	+	0.0916725i	$0.0292213\pi$
$858$	−31.7693	−	11.6962i	−1.08459	−	0.399302i
$859$	−18.4531	−	44.5498i	−0.629612	−	1.52002i	−0.840105	−	0.542423i	$-0.817507\pi$
$859$	−18.4531	−	44.5498i	−0.629612	−	1.52002i	0.210493	−	0.977595i	$-0.432493\pi$
$860$	12.3982	+	10.5605i	0.422776	+	0.360109i
$861$	28.7140	+	11.8937i	0.978571	+	0.405337i
$862$	−24.1057	+	0.963245i	−0.821043	+	0.0328083i
$863$	23.0704			0.785326			0.392663	−	0.919682i	$-0.371554\pi$
$863$	23.0704			0.785326			0.392663	+	0.919682i	$0.371554\pi$
$864$	−63.5105	+	42.7440i	−2.16067	+	1.45418i
$865$	22.7838			0.774674
$866$	−21.6382	+	0.864646i	−0.735296	+	0.0293819i
$867$	−46.0280	−	19.0654i	−1.56319	−	0.647496i
$868$	2.35898	−	2.76949i	0.0800689	−	0.0940027i
$869$	−3.77145	−	9.10508i	−0.127938	−	0.308869i
$870$	−23.5565	−	8.67256i	−0.798638	−	0.294027i
$871$	−26.7754	+	26.7754i	−0.907249	+	0.907249i
$872$	38.0018	+	10.6354i	1.28690	+	0.360161i
$873$	−26.0608	−	26.0608i	−0.882024	−	0.882024i
$874$	−20.8261	−	45.0959i	−0.704452	−	1.52539i
$875$	0.0655671	−	0.0271588i	0.00221657	−	0.000918134i
$876$	1.79591	+	3.51305i	0.0606780	+	0.118695i
$877$	0.109681	−	0.264794i	0.00370368	−	0.00894147i	−0.922017	−	0.387150i	$-0.873460\pi$
$877$	0.109681	−	0.264794i	0.00370368	−	0.00894147i	0.925721	+	0.378208i	$0.123460\pi$
$878$	10.5903	−	11.4718i	0.357404	−	0.387156i
$879$		−	80.4930i		−	2.71496i
$880$	21.1035	+	15.2466i	0.711398	+	0.513962i
$881$			11.6917i			0.393905i	0.980413	+	0.196952i	$0.0631044\pi$
$881$			11.6917i			0.393905i	−0.980413	+	0.196952i	$0.936896\pi$
$882$	−7.51391	−	6.93648i	−0.253006	−	0.233564i
$883$	−9.93442	+	23.9838i	−0.334320	+	0.807119i	0.663920	+	0.747804i	$0.268892\pi$
$883$	−9.93442	+	23.9838i	−0.334320	+	0.807119i	−0.998239	+	0.0593153i	$0.981108\pi$
$884$	−8.26696	−	2.67389i	−0.278048	−	0.0899327i
$885$	−76.6984	+	31.7695i	−2.57819	+	1.06792i
$886$	−39.5329	+	18.2569i	−1.32813	+	0.613354i
$887$	37.0865	+	37.0865i	1.24524	+	1.24524i	0.957797	+	0.287445i	$0.0928058\pi$
$887$	37.0865	+	37.0865i	1.24524	+	1.24524i	0.287445	+	0.957797i	$0.407194\pi$
$888$	81.8204	−	9.85041i	2.74571	−	0.330558i
$889$	−0.789983	+	0.789983i	−0.0264952	+	0.0264952i
$890$	19.4327	−	52.7831i	0.651384	−	1.76929i
$891$	−16.9895	−	41.0163i	−0.569169	−	1.37410i
$892$	2.81372	−	0.225228i	0.0942102	−	0.00754118i
$893$	6.41567	+	2.65746i	0.214692	+	0.0889285i
$894$	2.10896	+	52.7777i	0.0705341	+	1.76515i
$895$	−59.6922			−1.99529
$896$	9.89691	+	5.48189i	0.330633	+	0.183137i
$897$	78.6725			2.62680
$898$	−1.22104	−	30.5570i	−0.0407465	−	1.01970i
$899$	2.94576	+	1.22017i	0.0982465	+	0.0406950i
$900$	72.4022	−	5.79553i	2.41341	−	0.193184i
$901$	−2.60152	−	6.28062i	−0.0866691	−	0.209238i
$902$	9.76068	−	26.5120i	0.324995	−	0.882753i
$903$	−5.81763	+	5.81763i	−0.193599	+	0.193599i
$904$	12.7227	−	1.53170i	0.423152	−	0.0509435i
$905$	37.8344	+	37.8344i	1.25766	+	1.25766i
$906$	31.4998	−	14.5471i	1.04651	−	0.483296i
$907$	−39.6802	+	16.4361i	−1.31756	+	0.545751i	−0.927081	−	0.374862i	$-0.877690\pi$
$907$	−39.6802	+	16.4361i	−1.31756	+	0.545751i	−0.390478	+	0.920612i	$0.627690\pi$
$908$	11.7137	+	3.78872i	0.388733	+	0.125733i
$909$	9.95740	−	24.0393i	0.330266	−	0.797333i
$910$	11.9752	+	11.0549i	0.396975	+	0.366468i
$911$			35.7719i			1.18517i	0.805506	+	0.592587i	$0.201894\pi$
$911$			35.7719i			1.18517i	−0.805506	+	0.592587i	$0.798106\pi$
$912$	38.9493	−	53.9114i	1.28974	−	1.78519i
$913$			13.8480i			0.458301i
$914$	−38.1285	+	41.3025i	−1.26118	+	1.36617i
$915$	20.0070	−	48.3011i	0.661410	−	1.59678i
$916$	14.6453	+	28.6484i	0.483895	+	0.946569i
$917$	−14.3220	+	5.93236i	−0.472954	+	0.195904i
$918$	−9.57627	−	20.7361i	−0.316064	−	0.684393i
$919$	32.0045	+	32.0045i	1.05573	+	1.05573i	0.998353	+	0.0573783i	$0.0182741\pi$
$919$	32.0045	+	32.0045i	1.05573	+	1.05573i	0.0573783	+	0.998353i	$0.481726\pi$
$920$	−58.2632	−	16.3059i	−1.92088	−	0.537590i
$921$	44.6368	−	44.6368i	1.47083	−	1.47083i
$922$	−47.9812	−	17.6648i	−1.58018	−	0.581759i
$923$	−12.3493	−	29.8139i	−0.406483	−	0.981336i
$924$	−8.52828	+	10.0124i	−0.280560	+	0.329383i
$925$	−42.2680	−	17.5080i	−1.38976	−	0.575658i
$926$	−41.3685	+	1.65305i	−1.35945	+	0.0543227i
$927$	95.7682			3.14544
$928$	−1.90198	+	9.73166i	−0.0624354	+	0.319457i
$929$	−40.3385			−1.32346			−0.661732	−	0.749740i	$-0.730178\pi$
$929$	−40.3385			−1.32346			−0.661732	+	0.749740i	$0.730178\pi$
$930$	−26.0281	+	1.04006i	−0.853495	+	0.0341050i
$931$	4.80264	+	1.98932i	0.157400	+	0.0651972i
$932$	33.1242	+	28.2143i	1.08502	+	0.924191i
$933$	−32.1002	−	77.4968i	−1.05091	−	2.53713i
$934$	23.3851	+	8.60948i	0.765184	+	0.281711i
$935$	−5.49255	+	5.49255i	−0.179626	+	0.179626i
$936$	36.5083	+	64.8848i	1.19331	+	2.12083i
$937$	7.47713	+	7.47713i	0.244267	+	0.244267i	0.818613	−	0.574346i	$-0.194743\pi$
$937$	7.47713	+	7.47713i	0.244267	+	0.244267i	−0.574346	+	0.818613i	$0.694743\pi$
$938$	6.16777	+	13.3555i	0.201385	+	0.436071i
$939$	−88.7875	+	36.7770i	−2.89747	+	1.20017i
$940$	7.53119	−	3.85002i	0.245640	−	0.125574i
$941$	−2.51006	+	6.05981i	−0.0818255	+	0.197544i	−0.959497	−	0.281718i	$-0.909096\pi$
$941$	−2.51006	+	6.05981i	−0.0818255	+	0.197544i	0.877672	+	0.479262i	$0.159096\pi$
$942$	−16.5891	+	17.9701i	−0.540503	+	0.585497i
$943$			65.6535i			2.13797i
$944$	17.2092	+	27.9151i	0.560110	+	0.908558i
$945$			42.8434i			1.39369i
$946$	5.49518	+	5.07289i	0.178664	+	0.164934i
$947$	−9.79963	+	23.6584i	−0.318445	+	0.768795i	0.680892	+	0.732384i	$0.261592\pi$
$947$	−9.79963	+	23.6584i	−0.318445	+	0.768795i	−0.999337	+	0.0364108i	$0.988408\pi$
$948$	−9.43713	+	29.1771i	−0.306504	+	0.947628i
$949$	2.07422	−	0.859169i	0.0673319	−	0.0278898i
$950$	−33.5207	+	15.4804i	−1.08755	+	0.502250i
$951$	33.6396	+	33.6396i	1.09084	+	1.09084i
$952$	−2.08444	+	2.65503i	−0.0675571	+	0.0860499i
$953$	−0.480345	+	0.480345i	−0.0155599	+	0.0155599i	−0.714844	−	0.699284i	$-0.753502\pi$
$953$	−0.480345	+	0.480345i	−0.0155599	+	0.0155599i	0.699284	+	0.714844i	$0.253502\pi$
$954$	−20.1252	+	54.6641i	−0.651577	+	1.76982i
$955$	−1.23283	−	2.97632i	−0.0398936	−	0.0963116i
$956$	−2.21338	−	27.6512i	−0.0715858	−	0.894305i
$957$	−10.6496	−	4.41122i	−0.344254	−	0.142595i
$958$	0.458826	+	11.4824i	0.0148240	+	0.370978i
$959$	−19.1881			−0.619616
$960$	−19.2268	−	78.6945i	−0.620543	−	2.53985i
$961$	−27.6913			−0.893267
$962$	−1.87239	−	46.8575i	−0.0603683	−	1.51075i
$963$	105.003	+	43.4935i	3.38366	+	1.40156i
$964$	−1.85716	−	23.2011i	−0.0598152	−	0.747258i
$965$	−9.04004	−	21.8246i	−0.291009	−	0.702558i
$966$	10.5596	−	28.6820i	0.339749	−	0.922828i
$967$	12.0455	−	12.0455i	0.387356	−	0.387356i	−0.486387	−	0.873743i	$-0.661686\pi$
$967$	12.0455	−	12.0455i	0.387356	−	0.387356i	0.873743	+	0.486387i	$0.161686\pi$
$968$	−15.0683	−	11.8300i	−0.484314	−	0.380231i
$969$	14.0314	+	14.0314i	0.450754	+	0.450754i
$970$	20.7171	−	9.56748i	0.665185	−	0.307193i
$971$	14.6308	−	6.06027i	0.469524	−	0.194483i	−0.135360	−	0.990796i	$-0.543219\pi$
$971$	14.6308	−	6.06027i	0.469524	−	0.194483i	0.604885	+	0.796313i	$0.293219\pi$
$972$	−17.5235	+	54.1781i	−0.562067	+	1.73776i
$973$	−3.97854	+	9.60504i	−0.127546	+	0.307923i
$974$	−7.56560	−	6.98420i	−0.242417	−	0.223788i
$975$		−	58.4788i		−	1.87282i
$976$	−20.0940	−	4.76738i	−0.643192	−	0.152600i
$977$			29.9866i			0.959356i	0.877445	+	0.479678i	$0.159246\pi$
$977$			29.9866i			0.959356i	−0.877445	+	0.479678i	$0.840754\pi$
$978$	12.9177	−	13.9931i	0.413063	−	0.447449i
$979$	9.88425	−	23.8627i	0.315902	−	0.762655i
$980$	5.63769	−	2.88204i	0.180089	−	0.0920634i
$981$	93.2063	−	38.6073i	2.97585	−	1.23264i
$982$	17.0391	+	36.8959i	0.543740	+	1.17739i
$983$	37.5569	+	37.5569i	1.19788	+	1.19788i	0.974801	+	0.223077i	$0.0716101\pi$
$983$	37.5569	+	37.5569i	1.19788	+	1.19788i	0.223077	+	0.974801i	$0.428390\pi$
$984$	−76.6123	+	43.1069i	−2.44231	+	1.37420i
$985$	−1.71342	+	1.71342i	−0.0545940	+	0.0545940i
$986$	−2.77626	−	1.02211i	−0.0884140	−	0.0325506i
$987$	1.63516	+	3.94763i	0.0520478	+	0.125654i
$988$	−28.8112	−	24.5406i	−0.916608	−	0.780741i
$989$	−16.0567	−	6.65090i	−0.510573	−	0.211486i
$990$	66.5059	−	2.65752i	2.11369	−	0.0844617i
$991$	−18.2941			−0.581130			−0.290565	−	0.956855i	$-0.593843\pi$
$991$	−18.2941			−0.581130			−0.290565	+	0.956855i	$0.593843\pi$
$992$	2.04113	+	10.0853i	0.0648060	+	0.320208i
$993$	−39.2932			−1.24693
$994$	−12.5269	+	0.500567i	−0.397330	+	0.0158770i
$995$	−18.4152	−	7.62781i	−0.583800	−	0.241818i
$996$	27.9402	−	32.8024i	0.885319	−	1.03938i
$997$	5.19570	+	12.5435i	0.164549	+	0.397257i	0.984550	−	0.175106i	$-0.0560268\pi$
$997$	5.19570	+	12.5435i	0.164549	+	0.397257i	−0.820000	+	0.572363i	$0.806027\pi$
$998$	18.7709	+	6.91069i	0.594181	+	0.218754i
$999$	87.1697	−	87.1697i	2.75793	−	2.75793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.7	✓	52
4.3	odd	2		896.2.u.c.337.13		52
32.11	odd	8		896.2.u.c.561.13		52
32.21	even	8	inner	224.2.u.c.85.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.7	✓	52	1.1	even	1	trivial
224.2.u.c.85.7	yes	52	32.21	even	8	inner
896.2.u.c.337.13		52	4.3	odd	2
896.2.u.c.561.13		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0564658 - 1.41309i) q^{2} +(-2.95511 - 1.22405i) q^{3} +(-1.99362 + 0.159582i) q^{4} +(-1.21151 - 2.92484i) q^{5} +(-1.56282 + 4.24494i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.338075 + 2.80815i) q^{8} +(5.11306 + 5.11306i) q^{9} +O(q^{10})\)	\(q+(-0.0564658 - 1.41309i) q^{2} +(-2.95511 - 1.22405i) q^{3} +(-1.99362 + 0.159582i) q^{4} +(-1.21151 - 2.92484i) q^{5} +(-1.56282 + 4.24494i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.338075 + 2.80815i) q^{8} +(5.11306 + 5.11306i) q^{9} +(-4.06464 + 1.87712i) q^{10} +(-1.89943 + 0.786772i) q^{11} +(6.08671 + 1.96870i) q^{12} +(1.39305 - 3.36312i) q^{13} +(-1.03913 - 0.959275i) q^{14} +10.1262i q^{15} +(3.94907 - 0.636293i) q^{16} +1.19342i q^{17} +(6.93648 - 7.51391i) q^{18} +(-1.98932 + 4.80264i) q^{19} +(2.88204 + 5.63769i) q^{20} +(-2.95511 + 1.22405i) q^{21} +(1.21903 + 2.63964i) q^{22} +(-4.77774 - 4.77774i) q^{23} +(2.43826 - 8.71221i) q^{24} +(-3.55139 + 3.55139i) q^{25} +(-4.83104 - 1.77860i) q^{26} +(-5.17889 - 12.5030i) q^{27} +(-1.29686 + 1.52255i) q^{28} +(-1.61945 - 0.670798i) q^{29} +(14.3091 - 0.571782i) q^{30} -1.81899 q^{31} +(-1.12212 - 5.54444i) q^{32} +6.57608 q^{33} +(1.68641 - 0.0673876i) q^{34} +(-2.92484 - 1.21151i) q^{35} +(-11.0095 - 9.37757i) q^{36} +(3.48596 + 8.41586i) q^{37} +(6.89886 + 2.53989i) q^{38} +(-8.23324 + 8.23324i) q^{39} +(7.80380 - 4.39091i) q^{40} +(-6.87077 - 6.87077i) q^{41} +(1.89655 + 4.10671i) q^{42} +(2.37639 - 0.984335i) q^{43} +(3.66120 - 1.87164i) q^{44} +(8.76036 - 21.1494i) q^{45} +(-6.48158 + 7.02114i) q^{46} -1.33587i q^{47} +(-12.4488 - 2.95352i) q^{48} -1.00000i q^{49} +(5.21894 + 4.81788i) q^{50} +(1.46080 - 3.52669i) q^{51} +(-2.24052 + 6.92710i) q^{52} +(-5.26270 + 2.17988i) q^{53} +(-17.3753 + 8.02421i) q^{54} +(4.60236 + 4.60236i) q^{55} +(2.22472 + 1.74661i) q^{56} +(11.7573 - 11.7573i) q^{57} +(-0.856451 + 2.32630i) q^{58} +(3.13737 + 7.57428i) q^{59} +(-1.61595 - 20.1877i) q^{60} +(-4.76993 - 1.97577i) q^{61} +(0.102711 + 2.57039i) q^{62} +7.23096 q^{63} +(-7.77141 + 1.89873i) q^{64} -11.5243 q^{65} +(-0.371324 - 9.29257i) q^{66} +(-9.61034 - 3.98073i) q^{67} +(-0.190449 - 2.37923i) q^{68} +(8.27057 + 19.9669i) q^{69} +(-1.54681 + 4.20145i) q^{70} +(6.26846 - 6.26846i) q^{71} +(-12.6296 + 16.0868i) q^{72} +(0.436110 + 0.436110i) q^{73} +(11.6955 - 5.40117i) q^{74} +(14.8418 - 6.14767i) q^{75} +(3.19953 - 9.89210i) q^{76} +(-0.786772 + 1.89943i) q^{77} +(12.0992 + 11.1694i) q^{78} +4.79357i q^{79} +(-6.64538 - 10.7795i) q^{80} +21.5939i q^{81} +(-9.32102 + 10.0969i) q^{82} +(2.57761 - 6.22290i) q^{83} +(5.69604 - 2.91187i) q^{84} +(3.49056 - 1.44584i) q^{85} +(-1.52513 - 3.30247i) q^{86} +(3.96456 + 3.96456i) q^{87} +(-2.85152 - 5.06791i) q^{88} +(-8.88342 + 8.88342i) q^{89} +(-30.3806 - 11.1849i) q^{90} +(-1.39305 - 3.36312i) q^{91} +(10.2875 + 8.76257i) q^{92} +(5.37531 + 2.22652i) q^{93} +(-1.88769 + 0.0754308i) q^{94} +16.4570 q^{95} +(-3.47065 + 17.7580i) q^{96} -5.09690 q^{97} +(-1.41309 + 0.0564658i) q^{98} +(-13.7347 - 5.68912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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