LMFDB - Embedded newform 392.2.z.a.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$392 = 2^{3} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	392.z (of order $42$ , degree $12$ , 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29596 - 0.566107i) q^{2} +(0.502307 + 3.33259i) q^{3} +(1.35904 + 1.46731i) q^{4} +(-0.588711 - 0.231052i) q^{5} +(1.23563 - 4.60328i) q^{6} +(-1.76263 - 1.97310i) q^{7} +(-0.930618 - 2.67095i) q^{8} +(-7.98712 + 2.46370i) q^{9} +(0.632148 + 0.632709i) q^{10} +(-0.526052 + 1.70542i) q^{11} +(-4.20728 + 5.26618i) q^{12} +(-0.264361 + 0.0603387i) q^{13} +(1.16732 + 3.55491i) q^{14} +(0.474288 - 2.07799i) q^{15} +(-0.305995 + 3.98828i) q^{16} +(-4.13715 + 2.82066i) q^{17} +(11.7457 + 1.32870i) q^{18} +(1.56736 - 0.904917i) q^{19} +(-0.461060 - 1.17783i) q^{20} +(5.69015 - 6.86524i) q^{21} +(1.64719 - 1.91236i) q^{22} +(-1.95361 - 1.33195i) q^{23} +(8.43371 - 4.44300i) q^{24} +(-3.37206 - 3.12882i) q^{25} +(0.376761 + 0.0714601i) q^{26} +(-7.83563 - 16.2708i) q^{27} +(0.499652 - 5.26786i) q^{28} +(-4.18049 + 8.68089i) q^{29} +(-1.79103 + 2.42450i) q^{30} +(2.51248 - 4.35174i) q^{31} +(2.65435 - 4.99544i) q^{32} +(-5.94770 - 0.896471i) q^{33} +(6.95839 - 1.31340i) q^{34} +(0.581793 + 1.56885i) q^{35} +(-14.4699 - 8.37130i) q^{36} +(0.463012 - 0.0346979i) q^{37} +(-2.54352 + 0.285444i) q^{38} +(-0.333875 - 0.850699i) q^{39} +(-0.0692624 + 1.78744i) q^{40} +(3.40699 + 4.27223i) q^{41} +(-11.2607 + 5.67586i) q^{42} +(6.05352 + 4.82752i) q^{43} +(-3.21730 + 1.54586i) q^{44} +(5.27135 + 0.395033i) q^{45} +(1.77778 + 2.83211i) q^{46} +(6.04782 - 5.61156i) q^{47} +(-13.4450 + 0.983584i) q^{48} +(-0.786248 + 6.95570i) q^{49} +(2.59883 + 5.96379i) q^{50} +(-11.4782 - 12.3706i) q^{51} +(-0.447814 - 0.305897i) q^{52} +(-0.237185 - 0.0177745i) q^{53} +(0.943641 + 25.5222i) q^{54} +(0.703733 - 0.882453i) q^{55} +(-3.62971 + 6.54410i) q^{56} +(3.80301 + 4.76883i) q^{57} +(10.3321 - 8.88351i) q^{58} +(-9.81346 + 3.85150i) q^{59} +(3.69363 - 2.12815i) q^{60} +(-9.69900 + 0.726840i) q^{61} +(-5.71963 + 4.21736i) q^{62} +(18.9395 + 11.4168i) q^{63} +(-6.26790 + 4.97126i) q^{64} +(0.169574 + 0.0255591i) q^{65} +(7.20050 + 4.52883i) q^{66} +(5.49055 + 3.16997i) q^{67} +(-9.76136 - 2.23708i) q^{68} +(3.45753 - 7.17963i) q^{69} +(0.134153 - 2.36252i) q^{70} +(-10.3238 + 4.97166i) q^{71} +(14.0134 + 19.0404i) q^{72} +(1.95130 + 1.81054i) q^{73} +(-0.619690 - 0.217147i) q^{74} +(8.73326 - 12.8093i) q^{75} +(3.45791 + 1.06998i) q^{76} +(4.29220 - 1.96807i) q^{77} +(-0.0488974 + 1.29148i) q^{78} +(6.84879 + 11.8624i) q^{79} +(1.10164 - 2.27724i) q^{80} +(29.5699 - 20.1604i) q^{81} +(-1.99680 - 7.46538i) q^{82} +(-7.07139 - 1.61400i) q^{83} +(17.8066 - 0.980950i) q^{84} +(3.08730 - 0.704657i) q^{85} +(-5.11225 - 9.68323i) q^{86} +(-31.0297 - 9.57140i) q^{87} +(5.04463 - 0.182037i) q^{88} +(-6.70774 + 2.06906i) q^{89} +(-6.60785 - 3.49610i) q^{90} +(0.585026 + 0.415256i) q^{91} +(-0.700663 - 4.67673i) q^{92} +(15.7646 + 6.18715i) q^{93} +(-11.0145 + 3.84866i) q^{94} +(-1.13181 + 0.170592i) q^{95} +(17.9810 + 6.33662i) q^{96} -1.75051 q^{97} +(4.95663 - 8.56924i) q^{98} -14.9174i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100})$ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$ .

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.29596	−	0.566107i	−0.916385	−	0.400298i
$2$	−1.29596	−	0.566107i	−0.916385	−	0.400298i
$3$	0.502307	+	3.33259i	0.290007	+	1.92407i	0.373638	+	0.927575i	$0.378110\pi$
$3$	0.502307	+	3.33259i	0.290007	+	1.92407i	−0.0836307	+	0.996497i	$0.526652\pi$
$4$	1.35904	+	1.46731i	0.679522	+	0.733655i
$5$	−0.588711	−	0.231052i	−0.263279	−	0.103330i	0.230030	−	0.973184i	$-0.426118\pi$
$5$	−0.588711	−	0.231052i	−0.263279	−	0.103330i	−0.493309	+	0.869854i	$0.664213\pi$
$6$	1.23563	−	4.60328i	0.504445	−	1.87928i
$7$	−1.76263	−	1.97310i	−0.666213	−	0.745762i
$7$	−1.76263	−	1.97310i	−0.666213	−	0.745762i
$8$	−0.930618	−	2.67095i	−0.329023	−	0.944322i
$9$	−7.98712	+	2.46370i	−2.66237	+	0.821234i
$10$	0.632148	+	0.632709i	0.199903	+	0.200080i
$11$	−0.526052	+	1.70542i	−0.158611	+	0.514203i	−0.999641	−	0.0267846i	$-0.991473\pi$
$11$	−0.526052	+	1.70542i	−0.158611	+	0.514203i	0.841031	+	0.540988i	$0.181949\pi$
$12$	−4.20728	+	5.26618i	−1.21454	+	1.52021i
$13$	−0.264361	+	0.0603387i	−0.0733206	+	0.0167350i	−0.259024	−	0.965871i	$-0.583401\pi$
$13$	−0.264361	+	0.0603387i	−0.0733206	+	0.0167350i	0.185703	+	0.982606i	$0.440544\pi$
$14$	1.16732	+	3.55491i	0.311980	+	0.950089i
$15$	0.474288	−	2.07799i	0.122461	−	0.536535i
$16$	−0.305995	+	3.98828i	−0.0764988	+	0.997070i
$17$	−4.13715	+	2.82066i	−1.00341	+	0.684111i	−0.949283	−	0.314423i	$-0.898189\pi$
$17$	−4.13715	+	2.82066i	−1.00341	+	0.684111i	−0.0541235	+	0.998534i	$0.517236\pi$
$18$	11.7457	+	1.32870i	2.76850	+	0.313178i
$19$	1.56736	−	0.904917i	0.359577	−	0.207602i	−0.309318	−	0.950959i	$-0.600101\pi$
$19$	1.56736	−	0.904917i	0.359577	−	0.207602i	0.668895	+	0.743357i	$0.266767\pi$
$20$	−0.461060	−	1.17783i	−0.103096	−	0.263371i
$21$	5.69015	−	6.86524i	1.24169	−	1.49812i
$22$	1.64719	−	1.91236i	0.351183	−	0.407716i
$23$	−1.95361	−	1.33195i	−0.407356	−	0.277731i	0.342258	−	0.939606i	$-0.388808\pi$
$23$	−1.95361	−	1.33195i	−0.407356	−	0.277731i	−0.749614	+	0.661875i	$0.769761\pi$
$24$	8.43371	−	4.44300i	1.72152	−	0.906924i
$25$	−3.37206	−	3.12882i	−0.674413	−	0.625764i
$26$	0.376761	+	0.0714601i	0.0738889	+	0.0140145i
$27$	−7.83563	−	16.2708i	−1.50797	−	3.13133i
$28$	0.499652	−	5.26786i	0.0944253	−	0.995532i
$29$	−4.18049	+	8.68089i	−0.776298	+	1.61200i	0.0144781	+	0.999895i	$0.495391\pi$
$29$	−4.18049	+	8.68089i	−0.776298	+	1.61200i	−0.790776	+	0.612105i	$0.790323\pi$
$30$	−1.79103	+	2.42450i	−0.326995	+	0.442652i
$31$	2.51248	−	4.35174i	0.451254	−	0.781595i	−0.547210	−	0.836995i	$-0.684310\pi$
$31$	2.51248	−	4.35174i	0.451254	−	0.781595i	0.998464	+	0.0554000i	$0.0176434\pi$
$32$	2.65435	−	4.99544i	0.469228	−	0.883077i
$33$	−5.94770	−	0.896471i	−1.03536	−	0.156056i
$34$	6.95839	−	1.31340i	1.19335	−	0.225247i
$35$	0.581793	+	1.56885i	0.0983409	+	0.265183i
$36$	−14.4699	−	8.37130i	−2.41164	−	1.39522i
$37$	0.463012	−	0.0346979i	0.0761187	−	0.00570431i	−0.0366163	−	0.999329i	$-0.511658\pi$
$37$	0.463012	−	0.0346979i	0.0761187	−	0.00570431i	0.112735	+	0.993625i	$0.464039\pi$
$38$	−2.54352	+	0.285444i	−0.412614	+	0.0463052i
$39$	−0.333875	−	0.850699i	−0.0534627	−	0.136221i
$40$	−0.0692624	+	1.78744i	−0.0109514	+	0.282618i
$41$	3.40699	+	4.27223i	0.532083	+	0.667211i	0.973125	−	0.230276i	$-0.0739627\pi$
$41$	3.40699	+	4.27223i	0.532083	+	0.667211i	−0.441043	+	0.897486i	$0.645391\pi$
$42$	−11.2607	+	5.67586i	−1.73756	+	0.875804i
$43$	6.05352	+	4.82752i	0.923153	+	0.736190i	0.964812	−	0.262942i	$-0.0846928\pi$
$43$	6.05352	+	4.82752i	0.923153	+	0.736190i	−0.0416586	+	0.999132i	$0.513264\pi$
$44$	−3.21730	+	1.54586i	−0.485027	+	0.233047i
$45$	5.27135	+	0.395033i	0.785806	+	0.0588880i
$46$	1.77778	+	2.83211i	0.262120	+	0.417572i
$47$	6.04782	−	5.61156i	0.882165	−	0.818529i	−0.102183	−	0.994766i	$-0.532583\pi$
$47$	6.04782	−	5.61156i	0.882165	−	0.818529i	0.984348	+	0.176236i	$0.0563922\pi$
$48$	−13.4450	+	0.983584i	−1.94062	+	0.141968i
$49$	−0.786248	+	6.95570i	−0.112321	+	0.993672i
$50$	2.59883	+	5.96379i	0.367529	+	0.843407i
$51$	−11.4782	−	12.3706i	−1.60727	−	1.73223i
$52$	−0.447814	−	0.305897i	−0.0621007	−	0.0424203i
$53$	−0.237185	−	0.0177745i	−0.0325798	−	0.00244152i	0.0584302	−	0.998291i	$-0.481390\pi$
$53$	−0.237185	−	0.0177745i	−0.0325798	−	0.00244152i	−0.0910100	+	0.995850i	$0.529010\pi$
$54$	0.943641	+	25.5222i	0.128413	+	3.47314i
$55$	0.703733	−	0.882453i	0.0948913	−	0.118990i
$56$	−3.62971	+	6.54410i	−0.485040	+	0.874492i
$57$	3.80301	+	4.76883i	0.503721	+	0.631647i
$58$	10.3321	−	8.88351i	1.35667	−	1.16646i
$59$	−9.81346	+	3.85150i	−1.27760	+	0.501422i	−0.904542	−	0.426384i	$-0.859787\pi$
$59$	−9.81346	+	3.85150i	−1.27760	+	0.501422i	−0.373061	+	0.927807i	$0.621692\pi$
$60$	3.69363	−	2.12815i	0.476846	−	0.274744i
$61$	−9.69900	+	0.726840i	−1.24183	+	0.0930623i	−0.679391	−	0.733776i	$-0.737756\pi$
$61$	−9.69900	+	0.726840i	−1.24183	+	0.0930623i	−0.562439	+	0.826839i	$0.690137\pi$
$62$	−5.71963	+	4.21736i	−0.726394	+	0.535606i
$63$	18.9395	+	11.4168i	2.38615	+	1.43838i
$64$	−6.26790	+	4.97126i	−0.783488	+	0.621407i
$65$	0.169574	+	0.0255591i	0.0210330	+	0.00317022i
$66$	7.20050	+	4.52883i	0.886321	+	0.557461i
$67$	5.49055	+	3.16997i	0.670777	+	0.387273i	0.796371	−	0.604808i	$-0.206750\pi$
$67$	5.49055	+	3.16997i	0.670777	+	0.387273i	−0.125594	+	0.992082i	$0.540084\pi$
$68$	−9.76136	−	2.23708i	−1.18374	−	0.271285i
$69$	3.45753	−	7.17963i	0.416238	−	0.864326i
$70$	0.134153	−	2.36252i	0.0160343	−	0.282376i
$71$	−10.3238	+	4.97166i	−1.22521	+	0.590028i	−0.930757	−	0.365639i	$-0.880850\pi$
$71$	−10.3238	+	4.97166i	−1.22521	+	0.590028i	−0.294449	+	0.955667i	$0.595136\pi$
$72$	14.0134	+	19.0404i	1.65149	+	2.24393i
$73$	1.95130	+	1.81054i	0.228382	+	0.211908i	0.786061	−	0.618149i	$-0.212117\pi$
$73$	1.95130	+	1.81054i	0.228382	+	0.211908i	−0.557678	+	0.830057i	$0.688308\pi$
$74$	−0.619690	−	0.217147i	−0.0720374	−	0.0252429i
$75$	8.73326	−	12.8093i	1.00843	−	1.47909i
$76$	3.45791	+	1.06998i	0.396649	+	0.122735i
$77$	4.29220	−	1.96807i	0.489141	−	0.224283i
$78$	−0.0488974	+	1.29148i	−0.00553654	+	0.146232i
$79$	6.84879	+	11.8624i	0.770549	+	1.33463i	0.937262	+	0.348625i	$0.113351\pi$
$79$	6.84879	+	11.8624i	0.770549	+	1.33463i	−0.166714	+	0.986005i	$0.553316\pi$
$80$	1.10164	−	2.27724i	0.123167	−	0.254603i
$81$	29.5699	−	20.1604i	3.28554	−	2.24005i
$82$	−1.99680	−	7.46538i	−0.220509	−	0.824413i
$83$	−7.07139	−	1.61400i	−0.776186	−	0.177159i	−0.183962	−	0.982933i	$-0.558892\pi$
$83$	−7.07139	−	1.61400i	−0.776186	−	0.177159i	−0.592223	+	0.805774i	$0.701750\pi$
$84$	17.8066	−	0.980950i	1.94286	−	0.107030i
$85$	3.08730	−	0.704657i	0.334865	−	0.0764308i
$86$	−5.11225	−	9.68323i	−0.551268	−	1.04417i
$87$	−31.0297	−	9.57140i	−3.32674	−	1.02616i
$88$	5.04463	−	0.182037i	0.537760	−	0.0194052i
$89$	−6.70774	+	2.06906i	−0.711019	+	0.219320i	−0.629107	−	0.777319i	$-0.716579\pi$
$89$	−6.70774	+	2.06906i	−0.711019	+	0.219320i	−0.0819128	+	0.996640i	$0.526103\pi$
$90$	−6.60785	−	3.49610i	−0.696528	−	0.368521i
$91$	0.585026	+	0.415256i	0.0613274	+	0.0435307i
$92$	−0.700663	−	4.67673i	−0.0730491	−	0.487583i
$93$	15.7646	+	6.18715i	1.63471	+	0.641577i
$94$	−11.0145	+	3.84866i	−1.13606	+	0.396959i
$95$	−1.13181	+	0.170592i	−0.116121	+	0.0175024i
$96$	17.9810	+	6.33662i	1.83518	+	0.646729i
$97$	−1.75051			−0.177738			−0.0888688	−	0.996043i	$-0.528325\pi$
$97$	−1.75051			−0.177738			−0.0888688	+	0.996043i	$0.528325\pi$
$98$	4.95663	−	8.56924i	0.500695	−	0.865624i
$99$		−	14.9174i		−	1.49926i
$100$	0.00815938	−	9.20007i	0.000815938	−	0.920007i
$101$	1.02137	+	6.77638i	0.101631	+	0.674275i	0.980398	+	0.197025i	$0.0631281\pi$
$101$	1.02137	+	6.77638i	0.101631	+	0.674275i	−0.878768	+	0.477249i	$0.841634\pi$
$102$	7.87229	+	22.5297i	0.779472	+	2.23078i
$103$	2.24860	−	5.72934i	0.221561	−	0.564529i	−0.776267	−	0.630405i	$-0.782889\pi$
$103$	2.24860	−	5.72934i	0.221561	−	0.564529i	0.997828	+	0.0658761i	$0.0209842\pi$
$104$	0.407181	+	0.649942i	0.0399274	+	0.0637321i
$105$	−4.93608	+	2.72692i	−0.481712	+	0.266120i
$106$	0.297321	+	0.157307i	0.0288783	+	0.0152790i
$107$	4.73192	+	15.3405i	0.457452	+	1.48302i	0.831453	+	0.555596i	$0.187510\pi$
$107$	4.73192	+	15.3405i	0.457452	+	1.48302i	−0.374000	+	0.927429i	$0.622014\pi$
$108$	13.2254	−	33.6101i	1.27261	−	3.23413i
$109$	−0.272991	+	0.885016i	−0.0261478	+	0.0847692i	−0.967706	−	0.252080i	$-0.918885\pi$
$109$	−0.272991	+	0.885016i	−0.0261478	+	0.0847692i	0.941558	+	0.336850i	$0.109361\pi$
$110$	−1.41158	+	0.745239i	−0.134588	+	0.0710557i
$111$	0.348208	+	1.52560i	0.0330505	+	0.144804i
$112$	8.40863	−	6.42611i	0.794541	−	0.607211i
$113$	1.97189	−	8.63943i	0.185500	−	0.812730i	−0.793451	−	0.608634i	$-0.791718\pi$
$113$	1.97189	−	8.63943i	0.185500	−	0.812730i	0.978951	−	0.204095i	$-0.0654252\pi$
$114$	−2.22890	−	8.33314i	−0.208755	−	0.780470i
$115$	0.842362	+	1.23552i	0.0785507	+	0.115213i
$116$	−18.4190	+	5.66363i	−1.71016	+	0.525855i
$117$	1.96283	−	1.13324i	0.181464	−	0.104768i
$118$	14.8983	+	0.564069i	1.37150	+	0.0519268i
$119$	12.8577	+	3.19122i	1.17867	+	0.292539i
$120$	−5.99158	+	0.667018i	−0.546954	+	0.0608902i
$121$	6.45691	+	4.40224i	0.586991	+	0.400204i
$122$	12.9810	+	4.54872i	1.17525	+	0.411822i
$123$	−12.5262	+	13.5001i	−1.12945	+	1.21726i
$124$	9.79992	−	2.22763i	0.880059	−	0.200047i
$125$	2.63425	+	5.47008i	0.235615	+	0.489259i
$126$	−18.0818	−	25.5175i	−1.61085	−	2.27328i
$127$	−8.11505	−	3.90800i	−0.720094	−	0.346779i	0.0376853	−	0.999290i	$-0.488002\pi$
$127$	−8.11505	−	3.90800i	−0.720094	−	0.346779i	−0.757780	+	0.652510i	$0.773716\pi$
$128$	10.9372	−	2.89427i	0.966725	−	0.255819i
$129$	−13.0474	+	22.5988i	−1.14876	+	1.98971i
$130$	−0.205292	−	0.129121i	−0.0180053	−	0.0113246i
$131$	−0.990967	+	6.57464i	−0.0865812	+	0.574429i	0.902909	+	0.429831i	$0.141427\pi$
$131$	−0.990967	+	6.57464i	−0.0865812	+	0.574429i	−0.989491	+	0.144598i	$0.953811\pi$
$132$	−6.76779	−	9.94546i	−0.589060	−	0.865641i
$133$	−4.54817	−	1.49753i	−0.394377	−	0.129852i
$134$	−5.32101	−	7.21640i	−0.459665	−	0.623402i
$135$	0.853507	+	11.3893i	0.0734582	+	0.980231i
$136$	11.3839	+	8.42515i	0.976165	+	0.722450i
$137$	−0.422287	−	1.07597i	−0.0360784	−	0.0919263i	0.911699	−	0.410859i	$-0.134771\pi$
$137$	−0.422287	−	1.07597i	−0.0360784	−	0.0919263i	−0.947778	+	0.318932i	$0.896676\pi$
$138$	−8.54528	+	7.34721i	−0.727422	+	0.625436i
$139$	14.3989	−	11.4828i	1.22130	−	0.973956i	0.221303	−	0.975205i	$-0.428969\pi$
$139$	14.3989	−	11.4828i	1.22130	−	0.973956i	0.999999	+	0.00124864i	$0.000397454\pi$
$140$	−1.51130	+	2.98580i	−0.127728	+	0.252346i
$141$	21.7389	+	17.3362i	1.83074	+	1.45997i
$142$	16.1937	−	0.598735i	1.35895	−	0.0502448i
$143$	0.0361650	−	0.482588i	0.00302427	−	0.0403560i
$144$	−7.38191	−	32.6088i	−0.615159	−	2.71740i
$145$	4.46684	−	4.14462i	0.370951	−	0.344192i
$146$	−1.50385	−	3.45104i	−0.124460	−	0.285610i
$147$	−23.5754	+	0.873656i	−1.94447	+	0.0720579i
$148$	0.680167	+	0.632226i	0.0559093	+	0.0519686i
$149$	9.53429	+	10.2755i	0.781079	+	0.841803i	0.990712	−	0.135977i	$-0.0434173\pi$
$149$	9.53429	+	10.2755i	0.781079	+	0.841803i	−0.209633	+	0.977780i	$0.567227\pi$
$150$	−18.5694	+	11.6565i	−1.51619	+	0.951747i
$151$	−1.24769	+	16.6493i	−0.101536	+	1.35490i	0.680996	+	0.732288i	$0.261547\pi$
$151$	−1.24769	+	16.6493i	−0.101536	+	1.35490i	−0.782531	+	0.622611i	$0.786072\pi$
$152$	−3.87560	−	3.34421i	−0.314352	−	0.271251i
$153$	26.0947	−	32.7217i	2.10963	−	2.64539i
$154$	−6.67667	+	0.120708i	−0.538022	+	0.00972689i
$155$	−2.48460	+	1.98140i	−0.199568	+	0.159150i
$156$	0.794488	−	1.64604i	0.0636100	−	0.131788i
$157$	−13.6645	+	5.36292i	−1.09055	+	0.428008i	−0.841375	−	0.540452i	$-0.818253\pi$
$157$	−13.6645	+	5.36292i	−1.09055	+	0.428008i	−0.249171	+	0.968460i	$0.580158\pi$
$158$	−2.16036	−	19.2505i	−0.171869	−	1.53148i
$159$	−0.0599043	−	0.799368i	−0.00475072	−	0.0633940i
$160$	−2.71685	+	2.32758i	−0.214786	+	0.184011i
$161$	0.815430	+	6.20241i	0.0642649	+	0.488818i
$162$	−49.7345	+	9.38743i	−3.90751	+	0.737546i
$163$	−0.598033	+	3.96769i	−0.0468416	+	0.310774i	0.953125	+	0.302577i	$0.0978471\pi$
$163$	−0.598033	+	3.96769i	−0.0468416	+	0.310774i	−0.999966	+	0.00819625i	$0.997391\pi$
$164$	−1.63843	+	10.8053i	−0.127940	+	0.843749i
$165$	3.29434	+	1.90199i	0.256464	+	0.148070i
$166$	8.25057	+	6.09485i	0.640368	+	0.473052i
$167$	−14.8813	−	7.16648i	−1.15155	−	0.554559i	−0.242053	−	0.970263i	$-0.577821\pi$
$167$	−14.8813	−	7.16648i	−1.15155	−	0.554559i	−0.909500	+	0.415704i	$0.863535\pi$
$168$	−23.6320	−	8.80917i	−1.82325	−	0.679642i
$169$	−11.6463	+	5.60859i	−0.895873	+	0.431430i
$170$	−4.39995	−	0.834536i	−0.337461	−	0.0640060i
$171$	−10.2893	+	11.0892i	−0.786840	+	0.848012i
$172$	1.14354	+	15.4432i	0.0871938	+	1.17753i
$173$	1.83845	−	2.69651i	0.139775	−	0.205012i	−0.749968	−	0.661474i	$-0.769931\pi$
$173$	1.83845	−	2.69651i	0.139775	−	0.205012i	0.889743	+	0.456462i	$0.150884\pi$
$174$	34.7950	+	29.9704i	2.63780	+	2.27205i
$175$	−0.229760	+	12.1684i	−0.0173682	+	0.919843i
$176$	−6.64071	−	2.61989i	−0.500563	−	0.197482i
$177$	−17.7648	−	30.7696i	−1.33529	−	2.31278i
$178$	9.86431	+	1.11587i	0.739361	+	0.0836380i
$179$	−3.16134	−	4.63684i	−0.236290	−	0.346574i	0.689718	−	0.724078i	$-0.257735\pi$
$179$	−3.16134	−	4.63684i	−0.236290	−	0.346574i	−0.926008	+	0.377505i	$0.876782\pi$
$180$	6.58436	+	8.27157i	0.490769	+	0.616526i
$181$	−7.68037	−	1.75299i	−0.570877	−	0.130299i	−0.0726686	−	0.997356i	$-0.523152\pi$
$181$	−7.68037	−	1.75299i	−0.570877	−	0.130299i	−0.498209	+	0.867057i	$0.666009\pi$
$182$	−0.523093	−	0.869345i	−0.0387743	−	0.0644401i
$183$	−7.29414	−	31.9577i	−0.539198	−	2.36238i
$184$	−1.73950	+	6.45753i	−0.128238	+	0.476055i
$185$	−0.280597	−	0.0865528i	−0.0206299	−	0.00636349i
$186$	−16.9278	−	16.9428i	−1.24120	−	1.24230i
$187$	−2.63405	−	8.53939i	−0.192621	−	0.624462i
$188$	16.4531	+	1.24767i	1.19997	+	0.0909955i
$189$	−18.2927	+	44.1400i	−1.33060	+	3.21071i
$190$	1.56335	+	0.419642i	0.113418	+	0.0304440i
$191$	6.32366	−	16.1124i	0.457564	−	1.16585i	−0.496975	−	0.867765i	$-0.665556\pi$
$191$	6.32366	−	16.1124i	0.457564	−	1.16585i	0.954538	−	0.298088i	$-0.0963490\pi$
$192$	−19.7156	−	18.3912i	−1.42285	−	1.32727i
$193$	−8.24630	+	1.24293i	−0.593581	+	0.0894680i	−0.438961	−	0.898506i	$-0.644653\pi$
$193$	−8.24630	+	1.24293i	−0.593581	+	0.0894680i	−0.154620	+	0.987974i	$0.549415\pi$
$194$	2.26860	+	0.990978i	0.162876	+	0.0711481i
$195$			0.577958i			0.0413884i
$196$	−11.2747	+	8.29944i	−0.805337	+	0.592817i
$197$		−	6.71689i		−	0.478558i	−0.970951	−	0.239279i	$-0.923089\pi$
$197$		−	6.71689i		−	0.478558i	0.970951	−	0.239279i	$-0.0769111\pi$
$198$	−8.44486	+	19.3324i	−0.600150	+	1.37390i
$199$	21.7853	−	3.28361i	1.54432	−	0.232769i	0.679057	−	0.734085i	$-0.262389\pi$
$199$	21.7853	−	3.28361i	1.54432	−	0.232769i	0.865264	+	0.501316i	$0.167151\pi$
$200$	−5.21880	+	11.9183i	−0.369025	+	0.842753i
$201$	−7.80626	+	19.8900i	−0.550611	+	1.40294i
$202$	2.51249	−	9.36015i	0.176778	−	0.658578i
$203$	24.4969	−	7.05268i	1.71935	−	0.495001i
$204$	2.55206	−	33.6543i	0.178680	−	2.35627i
$205$	−1.01862	−	3.30230i	−0.0711439	−	0.230643i
$206$	−6.15753	+	6.15207i	−0.429015	+	0.428635i
$207$	18.8853	+	5.82533i	1.31262	+	0.404888i
$208$	−0.159754	−	1.07281i	−0.0110770	−	0.0743860i
$209$	0.718748	+	3.14904i	0.0497168	+	0.217824i
$210$	7.94071	−	0.739636i	0.547961	−	0.0510397i
$211$	3.05338	+	0.696915i	0.210204	+	0.0479776i	0.326326	−	0.945257i	$-0.394189\pi$
$211$	3.05338	+	0.696915i	0.210204	+	0.0479776i	−0.116122	+	0.993235i	$0.537046\pi$
$212$	−0.296264	−	0.372180i	−0.0203475	−	0.0255614i
$213$	−21.7542	−	31.9076i	−1.49057	−	2.18627i
$214$	2.55198	−	22.5595i	0.174450	−	1.54214i
$215$	−2.44836	−	4.24069i	−0.166977	−	0.289213i
$216$	−36.1666	+	36.0705i	−2.46082	+	2.45428i
$217$	−13.0150	+	2.71315i	−0.883515	+	0.184181i
$218$	0.854801	−	0.992407i	0.0578944	−	0.0672143i
$219$	−5.05364	+	7.41232i	−0.341493	+	0.500878i
$220$	2.25124	−	0.166699i	0.151778	−	0.0112389i
$221$	0.923507	−	0.995304i	0.0621218	−	0.0669514i
$222$	0.412388	−	2.17425i	0.0276777	−	0.145926i
$223$	−3.04048	+	1.46422i	−0.203606	+	0.0980514i	−0.532908	−	0.846173i	$-0.678901\pi$
$223$	−3.04048	+	1.46422i	−0.203606	+	0.0980514i	0.329302	+	0.944225i	$0.393187\pi$
$224$	−14.5352	+	3.56782i	−0.971171	+	0.238385i
$225$	34.6416	+	16.6825i	2.30944	+	1.11217i
$226$	−7.44635	+	10.0801i	−0.495324	+	0.670518i
$227$	6.94824	+	4.01157i	0.461171	+	0.266257i	0.712536	−	0.701635i	$-0.247546\pi$
$227$	6.94824	+	4.01157i	0.461171	+	0.266257i	−0.251366	+	0.967892i	$0.580880\pi$
$228$	−1.82888	+	12.0612i	−0.121121	+	0.798775i
$229$	3.85063	−	25.5472i	0.254457	−	1.68821i	−0.387820	−	0.921735i	$-0.626772\pi$
$229$	3.85063	−	25.5472i	0.254457	−	1.68821i	0.642276	−	0.766473i	$-0.277990\pi$
$230$	−0.392235	−	2.07806i	−0.0258632	−	0.137023i
$231$	8.71478	+	13.3156i	0.573391	+	0.876099i
$232$	27.0766	+	3.08729i	1.77767	+	0.202690i
$233$	1.20048	+	16.0193i	0.0786461	+	1.04946i	0.887306	+	0.461182i	$0.152574\pi$
$233$	1.20048	+	16.0193i	0.0786461	+	1.04946i	−0.808660	+	0.588277i	$0.799806\pi$
$234$	−3.18529	+	0.357466i	−0.208229	+	0.0233683i
$235$	−4.85698	+	1.90622i	−0.316834	+	0.124348i
$236$	−18.9883	−	9.16502i	−1.23603	−	0.596592i
$237$	−36.0925	+	28.7828i	−2.34446	+	1.86964i
$238$	−14.8566	−	11.4146i	−0.963009	−	0.739896i
$239$	16.3641	−	20.5200i	1.05851	−	1.32733i	0.115961	−	0.993254i	$-0.463005\pi$
$239$	16.3641	−	20.5200i	1.05851	−	1.32733i	0.942547	−	0.334073i	$-0.108423\pi$
$240$	8.14248	+	2.52745i	0.525595	+	0.163146i
$241$	−0.767700	+	10.2442i	−0.0494519	+	0.659890i	0.916312	+	0.400466i	$0.131152\pi$
$241$	−0.767700	+	10.2442i	−0.0494519	+	0.659890i	−0.965764	+	0.259424i	$0.916467\pi$
$242$	−5.87577	−	9.36045i	−0.377709	−	0.601713i
$243$	45.1893	+	48.7024i	2.89889	+	3.12426i
$244$	−14.2479	−	13.2436i	−0.912127	−	0.847837i
$245$	2.07000	−	3.91323i	0.132248	−	0.250007i
$246$	23.8760	−	10.4044i	1.52228	−	0.663361i
$247$	−0.359748	+	0.333797i	−0.0228902	+	0.0212390i
$248$	−13.9614	−	2.66089i	−0.886551	−	0.168966i
$249$	1.82679	−	24.3768i	0.115768	−	1.54481i
$250$	−0.317242	−	8.58030i	−0.0200641	−	0.542666i
$251$	17.2417	+	13.7498i	1.08829	+	0.867879i	0.991844	−	0.127459i	$-0.0406822\pi$
$251$	17.2417	+	13.7498i	1.08829	+	0.867879i	0.0964424	+	0.995339i	$0.469254\pi$
$252$	8.98765	+	43.3060i	0.566169	+	2.72802i
$253$	3.29923	−	2.63105i	0.207421	−	0.165413i
$254$	8.30446	+	9.65862i	0.521068	+	0.606036i
$255$	3.89911	+	9.93476i	0.244172	+	0.622139i
$256$	−15.8127	−	2.44079i	−0.988296	−	0.152549i
$257$	−1.00321	−	13.3869i	−0.0625785	−	0.835052i	−0.936876	−	0.349661i	$-0.886297\pi$
$257$	−1.00321	−	13.3869i	−0.0625785	−	0.835052i	0.874298	−	0.485390i	$-0.161322\pi$
$258$	29.7023	−	21.9010i	1.84919	−	1.36350i
$259$	−0.884583	−	0.852409i	−0.0549653	−	0.0529661i
$260$	0.192955	+	0.283553i	0.0119666	+	0.0175852i
$261$	12.0030	−	79.6348i	0.742968	−	4.92927i
$262$	5.00621	−	7.95950i	0.309285	−	0.491739i
$263$	1.15378	−	1.99841i	0.0711452	−	0.123227i	−0.828258	−	0.560347i	$-0.810668\pi$
$263$	1.15378	−	1.99841i	0.0711452	−	0.123227i	0.899403	+	0.437119i	$0.144001\pi$
$264$	3.14061	+	16.7203i	0.193291	+	1.02906i
$265$	0.135526	+	0.0652661i	0.00832532	+	0.00400926i
$266$	5.04651	+	4.51549i	0.309421	+	0.276863i
$267$	−10.2647	−	21.3148i	−0.628189	−	1.30445i
$268$	2.81057	+	12.3645i	0.171683	+	0.755280i
$269$	−13.6158	+	14.6743i	−0.830170	+	0.894711i	−0.995807	−	0.0914761i	$-0.970841\pi$
$269$	−13.6158	+	14.6743i	−0.830170	+	0.894711i	0.165637	+	0.986187i	$0.447032\pi$
$270$	5.34143	−	15.2432i	0.325069	−	0.927674i
$271$	−10.4861	−	7.14930i	−0.636985	−	0.434289i	0.201294	−	0.979531i	$-0.435485\pi$
$271$	−10.4861	−	7.14930i	−0.636985	−	0.434289i	−0.838279	+	0.545242i	$0.816438\pi$
$272$	−9.98364	−	17.3632i	−0.605347	−	1.05280i
$273$	−1.09002	+	2.15824i	−0.0659707	+	0.130623i
$274$	−0.0618458	+	1.63348i	−0.00373624	+	0.0986820i
$275$	7.10982	−	4.10486i	0.428739	−	0.247532i
$276$	15.2337	−	4.68418i	0.916960	−	0.281954i
$277$	−5.03894	−	7.39077i	−0.302761	−	0.444068i	0.644466	−	0.764633i	$-0.277080\pi$
$277$	−5.03894	−	7.39077i	−0.302761	−	0.444068i	−0.947227	+	0.320565i	$0.896127\pi$
$278$	−25.1610	+	6.72991i	−1.50906	+	0.403633i
$279$	−9.34608	+	40.9479i	−0.559535	+	2.45148i
$280$	3.64887	−	3.01393i	0.218062	−	0.180117i
$281$	−1.26034	−	5.52191i	−0.0751856	−	0.329410i	0.923322	−	0.384027i	$-0.125463\pi$
$281$	−1.26034	−	5.52191i	−0.0751856	−	0.329410i	−0.998507	+	0.0546177i	$0.982606\pi$
$282$	−18.3587	−	34.7736i	−1.09324	−	2.07074i
$283$	0.791004	−	2.56437i	0.0470203	−	0.152436i	−0.929018	−	0.370034i	$-0.879346\pi$
$283$	0.791004	−	2.56437i	0.0470203	−	0.152436i	0.976038	+	0.217598i	$0.0698222\pi$
$284$	−21.3254	−	8.39145i	−1.26543	−	0.497941i
$285$	−1.13703	−	3.68615i	−0.0673517	−	0.218349i
$286$	−0.320065	+	0.604943i	−0.0189258	+	0.0357710i
$287$	2.42427	−	14.2527i	0.143100	−	0.841311i
$288$	−8.89337	+	46.4387i	−0.524047	+	2.73643i
$289$	2.94909	−	7.51415i	0.173476	−	0.442009i
$290$	−8.13516	+	2.84257i	−0.477713	+	0.166921i
$291$	−0.879295	−	5.83374i	−0.0515452	−	0.341980i
$292$	−0.00472156	+	5.32376i	−0.000276308	+	0.311550i
$293$		−	1.13661i		−	0.0664013i	−0.999449	−	0.0332006i	$-0.989430\pi$
$293$		−	1.13661i		−	0.0664013i	0.999449	−	0.0332006i	$-0.0105700\pi$
$294$	31.0475	+	12.2140i	1.81073	+	0.712335i
$295$	6.66719			0.388179
$296$	−0.523564	−	1.20439i	−0.0304315	−	0.0700037i
$297$	31.8705	−	4.80371i	1.84932	−	0.278740i
$298$	−6.53905	−	18.7141i	−0.378797	−	1.08408i
$299$	0.596827	+	0.234237i	0.0345154	+	0.0135463i
$300$	30.6641	−	4.59407i	1.77040	−	0.265239i
$301$	−1.14495	−	20.4533i	−0.0659940	−	1.17891i
$302$	11.0422	−	20.8705i	0.635410	−	1.20096i
$303$	−22.0698	+	6.80764i	−1.26788	+	0.391089i
$304$	3.12945	+	6.52797i	0.179487	+	0.374405i
$305$	5.87785	+	1.81308i	0.336564	+	0.103816i
$306$	−52.3417	+	27.6337i	−2.99218	+	1.57971i
$307$	9.07260	−	2.07076i	0.517800	−	0.118185i	0.0443690	−	0.999015i	$-0.485872\pi$
$307$	9.07260	−	2.07076i	0.517800	−	0.118185i	0.473432	+	0.880831i	$0.343015\pi$
$308$	8.72106	+	3.62328i	0.496929	+	0.206456i
$309$	20.2230	+	4.61577i	1.15045	+	0.262582i
$310$	4.34164	−	1.16128i	0.246589	−	0.0659560i
$311$	13.8695	−	9.45608i	0.786468	−	0.536205i	−0.102195	−	0.994764i	$-0.532587\pi$
$311$	13.8695	−	9.45608i	0.786468	−	0.536205i	0.888664	+	0.458559i	$0.151634\pi$
$312$	−1.96146	+	1.68344i	−0.111046	+	0.0953059i
$313$	6.23031	+	10.7912i	0.352158	+	0.609955i	0.986627	−	0.162993i	$-0.0521147\pi$
$313$	6.23031	+	10.7912i	0.352158	+	0.609955i	−0.634469	+	0.772948i	$0.718781\pi$
$314$	20.7447	+	0.785423i	1.17069	+	0.0443240i
$315$	−8.51201	−	11.0972i	−0.479598	−	0.625256i
$316$	−8.09808	+	26.1709i	−0.455552	+	1.47223i
$317$	10.5085	−	15.4131i	0.590215	−	0.865687i	−0.408680	−	0.912678i	$-0.634011\pi$
$317$	10.5085	−	15.4131i	0.590215	−	0.865687i	0.998895	+	0.0469908i	$0.0149632\pi$
$318$	−0.374894	+	1.06986i	−0.0210230	+	0.0599950i
$319$	−12.6054	−	11.6961i	−0.705766	−	0.654855i
$320$	4.83860	−	1.47842i	0.270486	−	0.0826464i
$321$	−48.7468	+	23.4752i	−2.72078	+	1.31026i
$322$	2.45446	−	8.49972i	0.136782	−	0.473671i
$323$	−3.93195	+	8.16477i	−0.218779	+	0.454300i
$324$	69.7684	+	15.9893i	3.87602	+	0.888294i
$325$	1.08023	+	0.623672i	0.0599205	+	0.0345951i
$326$	3.02117	−	4.80343i	0.167327	−	0.266038i
$327$	−3.08652	−	0.465218i	−0.170685	−	0.0257266i
$328$	8.24029	−	13.0757i	0.454994	−	0.721985i
$329$	−21.7322	−	2.04184i	−1.19814	−	0.112570i
$330$	−3.19262	−	4.32986i	−0.175748	−	0.238351i
$331$	18.5243	−	1.38821i	1.01819	−	0.0763028i	0.444837	−	0.895611i	$-0.353262\pi$
$331$	18.5243	−	1.38821i	1.01819	−	0.0763028i	0.573353	+	0.819309i	$0.305643\pi$
$332$	−7.24210	−	12.5694i	−0.397462	−	0.689836i
$333$	−3.61265	+	1.41786i	−0.197972	+	0.0776982i
$334$	15.2287	+	17.7119i	0.833277	+	0.969154i
$335$	−2.49992	−	3.13480i	−0.136585	−	0.171272i
$336$	25.6393	+	24.7946i	1.39874	+	1.35266i
$337$	4.91627	−	6.16481i	0.267806	−	0.335819i	−0.629685	−	0.776851i	$-0.716816\pi$
$337$	4.91627	−	6.16481i	0.267806	−	0.335819i	0.897491	+	0.441032i	$0.145387\pi$
$338$	18.2683	−	0.675440i	0.993665	−	0.0367391i
$339$	29.7822	+	2.23187i	1.61755	+	0.121218i
$340$	5.22973	+	3.57237i	0.283622	+	0.193739i
$341$	6.09984	+	6.57407i	0.330325	+	0.356006i
$342$	19.6122	−	8.54636i	1.06051	−	0.462134i
$343$	15.1102	−	10.7090i	0.815872	−	0.578232i
$344$	7.26053	−	20.6612i	0.391462	−	1.11398i
$345$	−3.69435	+	3.42786i	−0.198897	+	0.184550i
$346$	−3.90908	+	2.45382i	−0.210153	+	0.131918i
$347$	−0.354114	−	0.0265371i	−0.0190098	−	0.00142459i	0.0652218	−	0.997871i	$-0.479225\pi$
$347$	−0.354114	−	0.0265371i	−0.0190098	−	0.00142459i	−0.0842316	+	0.996446i	$0.526844\pi$
$348$	−28.1266	−	58.5382i	−1.50774	−	3.13798i
$349$	−13.1753	−	10.5070i	−0.705259	−	0.562425i	0.203841	−	0.979004i	$-0.434658\pi$
$349$	−13.1753	−	10.5070i	−0.705259	−	0.562425i	−0.909100	+	0.416579i	$0.863229\pi$
$350$	7.18637	−	15.6397i	0.384128	−	0.835978i
$351$	3.05320	+	3.82859i	0.162968	+	0.204355i
$352$	7.12299	+	7.15464i	0.379656	+	0.381344i
$353$	9.79248	+	24.9508i	0.521201	+	1.32800i	0.913004	+	0.407950i	$0.133756\pi$
$353$	9.79248	+	24.9508i	0.521201	+	1.32800i	−0.391803	+	0.920049i	$0.628149\pi$
$354$	5.60369	+	49.9331i	0.297833	+	2.65391i
$355$	7.22642	−	0.541546i	0.383539	−	0.0287423i
$356$	−12.1521	−	7.03038i	−0.644059	−	0.372610i
$357$	−4.17650	+	44.4525i	−0.221044	+	2.35268i
$358$	1.47204	+	7.79884i	0.0777996	+	0.412181i
$359$	−2.71589	−	0.409355i	−0.143339	−	0.0216049i	0.0769805	−	0.997033i	$-0.475472\pi$
$359$	−2.71589	−	0.409355i	−0.143339	−	0.0216049i	−0.220320	+	0.975428i	$0.570710\pi$
$360$	−3.85050	−	14.4471i	−0.202939	−	0.761430i
$361$	−7.86225	+	13.6178i	−0.413803	+	0.716727i
$362$	8.96110	+	6.61973i	0.470985	+	0.347925i
$363$	−11.4275	+	23.7295i	−0.599789	+	1.24548i
$364$	0.185767	+	1.42277i	0.00973686	+	0.0745732i
$365$	−0.730422	−	1.51674i	−0.0382320	−	0.0793896i
$366$	−8.63855	+	45.5453i	−0.451544	+	2.38069i
$367$	−14.2028	−	13.1783i	−0.741379	−	0.687899i	0.216110	−	0.976369i	$-0.430663\pi$
$367$	−14.2028	−	13.1783i	−0.741379	−	0.687899i	−0.957489	+	0.288470i	$0.906853\pi$
$368$	5.90998	−	7.38398i	0.308079	−	0.384916i
$369$	−37.7376	−	25.7290i	−1.96454	−	1.33940i
$370$	0.314646	+	0.271017i	0.0163576	+	0.0140895i
$371$	0.382999	+	0.499319i	0.0198843	+	0.0259234i
$372$	12.3463	+	31.5402i	0.640127	+	1.63528i
$373$	−17.5161	+	10.1129i	−0.906947	+	0.523626i	−0.879448	−	0.475996i	$-0.842088\pi$
$373$	−17.5161	+	10.1129i	−0.906947	+	0.523626i	−0.0274993	+	0.999622i	$0.508754\pi$
$374$	−1.42057	+	12.5579i	−0.0734561	+	0.649353i
$375$	−16.9063	+	11.5265i	−0.873039	+	0.595228i
$376$	−20.6164	−	10.9312i	−1.06321	−	0.563733i
$377$	0.581367	−	2.54714i	0.0299419	−	0.131184i
$378$	48.6946	−	46.8482i	2.50458	−	2.40961i
$379$	−23.4026	+	5.34149i	−1.20211	+	0.274374i	−0.776256	−	0.630417i	$-0.782884\pi$
$379$	−23.4026	+	5.34149i	−1.20211	+	0.274374i	−0.425855	+	0.904791i	$0.640027\pi$
$380$	−1.78849	−	1.42887i	−0.0917474	−	0.0732993i
$381$	8.94752	−	29.0072i	0.458395	−	1.48608i
$382$	−17.3166	+	17.3012i	−0.885994	+	0.885208i
$383$	9.91708	−	3.05901i	0.506739	−	0.156308i	−0.0308356	−	0.999524i	$-0.509817\pi$
$383$	9.91708	−	3.05901i	0.506739	−	0.156308i	0.537575	+	0.843216i	$0.319341\pi$
$384$	15.1393	+	34.9955i	0.772572	+	1.78586i
$385$	−2.98159	+	0.166906i	−0.151956	+	0.00850630i
$386$	11.3905	+	3.05750i	0.579763	+	0.155623i
$387$	−60.2438	−	23.6439i	−3.06236	−	1.20189i
$388$	−2.37903	−	2.56854i	−0.120777	−	0.130398i
$389$	2.27310	+	15.0811i	0.115251	+	0.764640i	0.969556	+	0.244869i	$0.0787448\pi$
$389$	2.27310	+	15.0811i	0.115251	+	0.764640i	−0.854305	+	0.519772i	$0.826017\pi$
$390$	0.327186	−	0.749013i	0.0165677	−	0.0379277i
$391$	11.8394			0.598742
$392$	19.3100	−	4.37308i	0.975302	−	0.220874i
$393$	−22.4083			−1.13035
$394$	−3.80248	+	8.70484i	−0.191566	+	0.438544i
$395$	−1.29111	−	8.56598i	−0.0649630	−	0.431001i
$396$	21.8885	−	20.2734i	1.09994	−	1.01878i
$397$	3.92542	+	1.54061i	0.197011	+	0.0773211i	0.461795	−	0.886987i	$-0.347205\pi$
$397$	3.92542	+	1.54061i	0.197011	+	0.0773211i	−0.264784	+	0.964308i	$0.585301\pi$
$398$	−30.0919	−	8.07740i	−1.50837	−	0.404883i
$399$	2.70606	−	15.9094i	0.135472	−	0.796467i
$400$	13.5104	−	12.4913i	0.675522	−	0.624566i
$401$	5.06848	−	1.56342i	0.253108	−	0.0780735i	−0.165605	−	0.986192i	$-0.552958\pi$
$401$	5.06848	−	1.56342i	0.253108	−	0.0780735i	0.418713	+	0.908119i	$0.362481\pi$
$402$	21.3765	−	21.3576i	1.06616	−	1.06522i
$403$	−0.401623	+	1.30203i	−0.0200063	+	0.0648588i
$404$	−8.55495	+	10.7081i	−0.425625	+	0.532746i
$405$	−22.0662	+	5.03647i	−1.09648	+	0.250264i
$406$	−35.7397	−	4.72788i	−1.77373	−	0.234641i
$407$	−0.184394	+	0.807882i	−0.00914006	+	0.0400452i
$408$	−22.3593	+	42.1700i	−1.10695	+	2.08773i
$409$	28.8273	−	19.6541i	1.42542	−	0.971835i	0.427730	−	0.903906i	$-0.359313\pi$
$409$	28.8273	−	19.6541i	1.42542	−	0.971835i	0.997690	−	0.0679287i	$-0.0216390\pi$
$410$	−0.549356	+	4.85631i	−0.0271308	+	0.239836i
$411$	3.37365	−	1.94778i	0.166410	−	0.0960768i
$412$	11.4627	−	4.48704i	0.564725	−	0.221060i
$413$	24.8969	+	12.5742i	1.22510	+	0.618734i
$414$	−21.1769	−	18.2405i	−1.04079	−	0.896472i
$415$	3.79008	+	2.58404i	0.186048	+	0.126845i
$416$	−0.400290	+	1.48076i	−0.0196258	+	0.0726003i
$417$	45.5001	+	42.2179i	2.22815	+	2.06742i
$418$	0.851224	−	4.48793i	0.0416347	−	0.219512i
$419$	−13.9241	−	28.9138i	−0.680239	−	1.41253i	−0.899524	−	0.436870i	$-0.856087\pi$
$419$	−13.9241	−	28.9138i	−0.680239	−	1.41253i	0.219285	−	0.975661i	$-0.429627\pi$
$420$	−10.7096	−	3.53675i	−0.522574	−	0.172576i
$421$	−11.0103	+	22.8631i	−0.536608	+	1.11428i	0.439750	+	0.898120i	$0.355067\pi$
$421$	−11.0103	+	22.8631i	−0.536608	+	1.11428i	−0.976358	+	0.216158i	$0.930647\pi$
$422$	−3.56254	−	2.63172i	−0.173422	−	0.128110i
$423$	−34.4795	+	59.7202i	−1.67645	+	2.90370i
$424$	0.173254	+	0.650049i	0.00841394	+	0.0315692i
$425$	22.7761	+	3.43294i	1.10480	+	0.166522i
$426$	10.1296	+	53.6663i	0.490779	+	2.60014i
$427$	18.5299	+	17.8560i	0.896725	+	0.864110i
$428$	−16.0784	+	27.7917i	−0.777179	+	1.34336i
$429$	1.62643	−	0.121884i	0.0785249	−	0.00588463i
$430$	0.772305	+	6.88182i	0.0372438	+	0.331871i
$431$	12.5663	+	32.0183i	0.605296	+	1.54227i	0.824067	+	0.566493i	$0.191700\pi$
$431$	12.5663	+	32.0183i	0.605296	+	1.54227i	−0.218771	+	0.975776i	$0.570205\pi$
$432$	67.2903	−	26.2719i	3.23751	−	1.26401i
$433$	−0.762756	−	0.956465i	−0.0366557	−	0.0459648i	0.763166	−	0.646203i	$-0.223644\pi$
$433$	−0.762756	−	0.956465i	−0.0366557	−	0.0459648i	−0.799821	+	0.600238i	$0.795073\pi$
$434$	18.4029	+	3.85174i	0.883367	+	0.184889i
$435$	16.0560	+	12.8043i	0.769828	+	0.613918i
$436$	−1.66960	+	0.802214i	−0.0799594	+	0.0384191i
$437$	−4.26732	−	0.319791i	−0.204134	−	0.0152977i
$438$	10.7455	−	6.74520i	0.513440	−	0.322298i
$439$	−18.8173	+	17.4599i	−0.898103	+	0.833318i	−0.986667	−	0.162753i	$-0.947963\pi$
$439$	−18.8173	+	17.4599i	−0.898103	+	0.833318i	0.0885641	+	0.996070i	$0.471772\pi$
$440$	−3.01189	−	1.05841i	−0.143586	−	0.0504575i
$441$	−10.8569	−	57.4931i	−0.516996	−	2.73777i
$442$	−1.76028	+	0.767074i	−0.0837280	+	0.0364860i
$443$	−20.0089	−	21.5644i	−0.950650	−	1.02456i	−0.999668	−	0.0257589i	$-0.991800\pi$
$443$	−20.0089	−	21.5644i	−0.950650	−	1.02456i	0.0490184	−	0.998798i	$-0.484391\pi$
$444$	−1.76530	+	2.58429i	−0.0837773	+	0.122645i
$445$	4.42698	+	0.331756i	0.209859	+	0.0157268i
$446$	4.76926	−	0.176335i	0.225831	−	0.00834972i
$447$	−29.4550	+	36.9353i	−1.39317	+	1.74698i
$448$	20.8568	+	3.60469i	0.985391	+	0.170306i
$449$	−16.9332	−	21.2336i	−0.799128	−	1.00208i	−0.999749	−	0.0224063i	$-0.992867\pi$
$449$	−16.9332	−	21.2336i	−0.799128	−	1.00208i	0.200621	−	0.979669i	$-0.435704\pi$
$450$	−35.4501	−	41.2308i	−1.67113	−	1.94364i
$451$	−9.07820	+	3.56293i	−0.427476	+	0.167772i
$452$	15.3566	−	8.84800i	0.722315	−	0.416175i
$453$	−56.1119	+	4.20501i	−2.63637	+	0.197568i
$454$	−6.73369	−	9.13230i	−0.316028	−	0.428600i
$455$	−0.248466	−	0.379637i	−0.0116482	−	0.0177977i
$456$	9.19813	−	14.5956i	0.430742	−	0.683501i
$457$	27.8801	+	4.20225i	1.30418	+	0.196573i	0.764130	−	0.645062i	$-0.223169\pi$
$457$	27.8801	+	4.20225i	1.30418	+	0.196573i	0.540046	+	0.841635i	$0.318407\pi$
$458$	−19.4528	+	30.9284i	−0.908967	+	1.44519i
$459$	78.3117	+	45.2133i	3.65528	+	2.11038i
$460$	−0.668080	+	2.91513i	−0.0311494	+	0.135919i
$461$	5.20052	−	10.7990i	0.242213	−	0.502960i	−0.744054	−	0.668119i	$-0.767100\pi$
$461$	5.20052	−	10.7990i	0.242213	−	0.502960i	0.986267	+	0.165160i	$0.0528139\pi$
$462$	−3.75601	−	22.1900i	−0.174745	−	1.03237i
$463$	−4.84889	+	2.33510i	−0.225347	+	0.108521i	−0.543151	−	0.839635i	$-0.682769\pi$
$463$	−4.84889	+	2.33510i	−0.225347	+	0.108521i	0.317804	+	0.948156i	$0.397055\pi$
$464$	−33.3426	−	19.3293i	−1.54789	−	0.897340i
$465$	−7.85124	−	7.28488i	−0.364092	−	0.337828i
$466$	7.51286	−	21.4400i	0.348027	−	0.993190i
$467$	4.24815	−	6.23089i	0.196581	−	0.288331i	−0.715274	−	0.698844i	$-0.753698\pi$
$467$	4.24815	−	6.23089i	0.196581	−	0.288331i	0.911855	+	0.410513i	$0.134650\pi$
$468$	4.33039	+	1.33995i	0.200172	+	0.0619394i
$469$	−3.42315	−	16.4209i	−0.158067	−	0.758246i
$470$	7.37359	+	0.279175i	0.340119	+	0.0128774i
$471$	−24.7362	−	42.8443i	−1.13978	−	1.97416i
$472$	19.4197	+	22.6269i	0.893865	+	1.04149i
$473$	−11.4174	+	7.78426i	−0.524973	+	0.357920i
$474$	63.0687	−	16.8692i	2.89684	−	0.774830i
$475$	−8.11656	−	1.85255i	−0.372413	−	0.0850009i
$476$	12.7917	+	23.2033i	0.586307	+	1.06352i
$477$	1.93821	−	0.442385i	0.0887448	−	0.0202554i
$478$	−32.8238	+	17.3293i	−1.50133	+	0.792623i
$479$	17.1770	+	5.29842i	0.784839	+	0.242091i	0.661173	−	0.750233i	$-0.270059\pi$
$479$	17.1770	+	5.29842i	0.784839	+	0.242091i	0.123666	+	0.992324i	$0.460535\pi$
$480$	−9.12155	−	7.88500i	−0.416340	−	0.359899i
$481$	−0.120309	+	0.0371103i	−0.00548561	+	0.00169209i
$482$	6.79426	−	12.8416i	0.309470	−	0.584918i
$483$	−20.2605	+	5.83301i	−0.921884	+	0.265411i
$484$	2.31577	+	15.4571i	0.105262	+	0.702597i
$485$	1.03055	+	0.404459i	0.0467947	+	0.0183656i
$486$	−30.9928	−	88.6986i	−1.40586	−	4.02345i
$487$	−12.2920	+	1.85271i	−0.557002	+	0.0839545i	−0.421510	−	0.906824i	$-0.638500\pi$
$487$	−12.2920	+	1.85271i	−0.557002	+	0.0839545i	−0.135492	+	0.990778i	$0.543262\pi$
$488$	10.9674	+	25.2291i	0.496472	+	1.14207i
$489$	−13.5231			−0.611535
$490$	−4.89796	+	3.89957i	−0.221267	+	0.176164i
$491$		−	2.54800i		−	0.114990i	−0.998346	−	0.0574948i	$-0.981689\pi$
$491$		−	2.54800i		−	0.114990i	0.998346	−	0.0574948i	$-0.0183112\pi$
$492$	−36.8325	−	0.0326661i	−1.66054	−	0.00147270i
$493$	−7.19051	−	47.7059i	−0.323844	−	2.14857i
$494$	0.655186	−	0.228933i	0.0294782	−	0.0103002i
$495$	−3.44670	+	8.78205i	−0.154918	+	0.394724i
$496$	16.5871	+	11.3521i	0.744785	+	0.509723i
$497$	28.0066	+	11.6066i	1.25627	+	0.520627i
$498$	−16.1673	+	30.5572i	−0.724474	+	1.36930i
$499$	6.69900	+	21.7176i	0.299888	+	0.972214i	0.972634	+	0.232341i	$0.0746385\pi$
$499$	6.69900	+	21.7176i	0.299888	+	0.972214i	−0.672746	+	0.739874i	$0.734885\pi$
$500$	−4.44624	+	11.2993i	−0.198842	+	0.505322i
$501$	16.4079	−	53.1932i	0.733052	−	2.37650i
$502$	−14.5608	−	27.5799i	−0.649878	−	1.23095i
$503$	−5.64519	−	24.7332i	−0.251707	−	1.10280i	−0.929870	−	0.367888i	$-0.880081\pi$
$503$	−5.64519	−	24.7332i	−0.251707	−	1.10280i	0.678164	−	0.734911i	$-0.262776\pi$
$504$	12.8682	−	61.2110i	0.573195	−	2.72656i
$505$	0.964401	−	4.22532i	0.0429153	−	0.188024i
$506$	−5.76514	+	1.54203i	−0.256292	+	0.0685514i
$507$	−24.5412	−	35.9953i	−1.08991	−	1.59861i
$508$	−5.29447	−	17.2184i	−0.234904	−	0.763945i
$509$	8.63069	−	4.98293i	0.382549	−	0.220864i	−0.296378	−	0.955071i	$-0.595779\pi$
$509$	8.63069	−	4.98293i	0.382549	−	0.220864i	0.678927	+	0.734206i	$0.262445\pi$
$510$	0.571042	−	15.0824i	0.0252861	−	0.667860i
$511$	0.132954	−	7.04143i	0.00588154	−	0.311494i
$512$	19.1110	+	12.1149i	0.844594	+	0.535407i
$513$	−27.0050	−	18.4117i	−1.19230	−	0.812897i
$514$	−6.27830	+	17.9169i	−0.276924	+	0.790279i
$515$	−2.64755	+	2.85338i	−0.116665	+	0.125735i
$516$	−50.8915	+	11.5682i	−2.24037	+	0.509260i
$517$	6.38858	+	13.2660i	0.280970	+	0.583439i
$518$	0.663832	+	1.60546i	0.0291671	+	0.0705399i
$519$	9.90983	+	4.77232i	0.434993	+	0.209482i
$520$	−0.0895413	−	0.476708i	−0.00392665	−	0.0209050i
$521$	0.895757	−	1.55150i	0.0392438	−	0.0679723i	−0.845736	−	0.533601i	$-0.820838\pi$
$521$	0.895757	−	1.55150i	0.0392438	−	0.0679723i	0.884980	+	0.465629i	$0.154172\pi$
$522$	−60.6373	+	96.4088i	−2.65402	+	4.21970i
$523$	1.23823	−	8.21509i	0.0541438	−	0.359221i	−0.945310	−	0.326173i	$-0.894241\pi$
$523$	1.23823	−	8.21509i	0.0541438	−	0.359221i	0.999454	−	0.0330474i	$-0.0105212\pi$
$524$	−10.9938	+	7.48117i	−0.480266	+	0.326816i
$525$	−40.6676	+	5.34657i	−1.77488	+	0.233343i
$526$	−2.62657	+	1.93670i	−0.114524	+	0.0844441i
$527$	1.88028	+	25.0906i	0.0819065	+	1.09297i
$528$	5.39534	−	23.4468i	0.234802	−	1.02039i
$529$	−6.36034	−	16.2059i	−0.276536	−	0.704603i
$530$	−0.138690	−	0.161305i	−0.00602429	−	0.00700664i
$531$	68.8924	−	54.9398i	2.98967	−	2.38419i
$532$	−3.98384	−	8.70878i	−0.172721	−	0.377574i
$533$	−1.15846	−	0.923839i	−0.0501784	−	0.0400159i
$534$	1.23617	+	33.4342i	0.0534944	+	1.44684i
$535$	0.758723	−	10.1245i	0.0328024	−	0.437718i
$536$	3.35721	−	17.6150i	0.145010	−	0.760851i
$537$	13.8647	−	12.8646i	0.598307	−	0.555148i
$538$	25.9528	−	11.3094i	1.11891	−	0.487583i
$539$	−11.4488	−	4.99994i	−0.493134	−	0.215363i
$540$	−15.5516	+	16.7309i	−0.669235	+	0.719982i
$541$	−8.50874	−	9.17024i	−0.365819	−	0.394259i	0.523139	−	0.852247i	$-0.324761\pi$
$541$	−8.50874	−	9.17024i	−0.365819	−	0.394259i	−0.888958	+	0.457988i	$0.848570\pi$
$542$	9.54233	+	15.2015i	0.409878	+	0.652960i
$543$	1.98411	−	26.4761i	0.0851462	−	1.13620i
$544$	3.10898	+	28.1539i	0.133297	+	1.20709i
$545$	0.365198	−	0.457943i	0.0156434	−	0.0196161i
$546$	2.63442	−	2.17993i	0.112743	−	0.0932925i
$547$	16.0214	−	12.7766i	0.685025	−	0.546289i	−0.217962	−	0.975957i	$-0.569941\pi$
$547$	16.0214	−	12.7766i	0.685025	−	0.546289i	0.902987	+	0.429668i	$0.141369\pi$
$548$	1.00487	−	2.08192i	0.0429261	−	0.0889351i
$549$	75.6764	−	29.7008i	3.22979	−	1.26760i
$550$	−11.5379	+	1.29482i	−0.491976	+	0.0552115i
$551$	1.30313	+	17.3891i	0.0555153	+	0.740800i
$552$	−22.3940	−	2.55338i	−0.953154	−	0.108679i
$553$	11.3339	−	34.4225i	0.481966	−	1.46379i
$554$	2.34632	+	12.4308i	0.0996854	+	0.528132i
$555$	0.147499	−	0.978591i	0.00626098	−	0.0415389i
$556$	36.4176	+	5.52211i	1.54445	+	0.234189i
$557$	−20.2596	−	11.6969i	−0.858427	−	0.495613i	0.00505838	−	0.999987i	$-0.498390\pi$
$557$	−20.2596	−	11.6969i	−0.858427	−	0.495613i	−0.863485	+	0.504374i	$0.831723\pi$
$558$	35.2931	−	47.7761i	1.49408	−	2.02252i
$559$	−1.89160	−	0.910948i	−0.0800063	−	0.0385290i
$560$	−6.43502	+	1.84029i	−0.271929	+	0.0777665i
$561$	27.1352	−	13.0676i	1.14565	−	0.551715i
$562$	−1.49264	+	7.86968i	−0.0629632	+	0.331963i
$563$	−18.8889	+	20.3574i	−0.796071	+	0.857960i	−0.992460	−	0.122566i	$-0.960888\pi$
$563$	−18.8889	+	20.3574i	−0.796071	+	0.857960i	0.196390	+	0.980526i	$0.437078\pi$
$564$	4.10657	+	55.4583i	0.172918	+	2.33522i
$565$	−3.15703	+	4.63052i	−0.132817	+	0.194807i
$566$	−2.47682	+	2.87554i	−0.104109	+	0.120868i
$567$	−91.8994	−	22.8089i	−3.85941	−	0.957886i
$568$	22.8865	+	22.9475i	0.960297	+	0.962856i
$569$	11.6311	+	20.1456i	0.487600	+	0.844547i	0.999898	−	0.0142600i	$-0.00453926\pi$
$569$	11.6311	+	20.1456i	0.487600	+	0.844547i	−0.512299	+	0.858807i	$0.671206\pi$
$570$	−0.613212	+	5.42080i	−0.0256846	+	0.227052i
$571$	20.6897	+	30.3462i	0.865837	+	1.26995i	0.961575	+	0.274543i	$0.0885265\pi$
$571$	20.6897	+	30.3462i	0.865837	+	1.26995i	−0.0957381	+	0.995407i	$0.530521\pi$
$572$	0.757256	−	0.602793i	0.0316624	−	0.0252040i
$573$	56.8725	+	12.9808i	2.37588	+	0.542280i
$574$	−11.2103	+	17.0986i	−0.467910	+	0.713682i
$575$	2.42027	+	10.6039i	0.100932	+	0.442214i
$576$	37.8148	−	55.1483i	1.57562	−	2.29785i
$577$	−20.5601	−	6.34196i	−0.855929	−	0.264019i	−0.164423	−	0.986390i	$-0.552576\pi$
$577$	−20.5601	−	6.34196i	−0.855929	−	0.264019i	−0.691506	+	0.722371i	$0.743052\pi$
$578$	−8.07572	+	8.06856i	−0.335906	+	0.335608i
$579$	−8.28435	−	26.8572i	−0.344286	−	1.11615i
$580$	12.1521	+	0.921511i	0.504587	+	0.0382637i
$581$	9.27968	+	16.7974i	0.384986	+	0.696875i
$582$	−2.16299	+	8.05809i	−0.0896588	+	0.334019i
$583$	0.155084	−	0.395149i	0.00642294	−	0.0163654i
$584$	3.01994	−	6.89673i	0.124966	−	0.285389i
$585$	−1.41738	+	0.213635i	−0.0586013	+	0.00883272i
$586$	−0.643441	+	1.47300i	−0.0265803	+	0.0608491i
$587$			19.8324i			0.818570i	0.912407	+	0.409285i	$0.134222\pi$
$587$			19.8324i			0.818570i	−0.912407	+	0.409285i	$0.865778\pi$
$588$	−33.3220	−	33.4051i	−1.37418	−	1.37760i
$589$		−	9.09433i		−	0.374725i
$590$	−8.64043	−	3.77434i	−0.355721	−	0.155387i
$591$	22.3846	−	3.37394i	0.920781	−	0.138785i
$592$	−0.00329431	+	1.85724i	−0.000135395	+	0.0763320i
$593$	12.0089	−	30.5982i	0.493147	−	1.25652i	−0.440316	−	0.897843i	$-0.645134\pi$
$593$	12.0089	−	30.5982i	0.493147	−	1.25652i	0.933463	−	0.358674i	$-0.116771\pi$
$594$	−44.0225	−	11.8167i	−1.80626	−	0.484846i
$595$	−6.83214	−	4.84951i	−0.280091	−	0.198810i
$596$	−2.11984	+	27.9546i	−0.0868322	+	1.14507i
$597$	21.8859	+	70.9522i	0.895728	+	2.90388i
$598$	−0.640863	−	0.641432i	−0.0262068	−	0.0262301i
$599$	34.3530	+	10.5965i	1.40363	+	0.432961i	0.901855	−	0.432040i	$-0.142206\pi$
$599$	34.3530	+	10.5965i	1.40363	+	0.432961i	0.501771	+	0.865001i	$0.332682\pi$
$600$	−42.3404	−	11.4055i	−1.72854	−	0.465626i
$601$	2.23514	+	9.79280i	0.0911734	+	0.399457i	0.999837	−	0.0180730i	$-0.00575313\pi$
$601$	2.23514	+	9.79280i	0.0911734	+	0.399457i	−0.908663	+	0.417530i	$0.862896\pi$
$602$	−10.0950	+	27.1550i	−0.411440	+	1.10675i
$603$	−51.6635	−	11.7919i	−2.10390	−	0.480202i
$604$	−26.1253	+	20.7964i	−1.06302	+	0.846192i
$605$	−2.78410	−	4.08353i	−0.113190	−	0.166019i
$606$	32.4556	+	3.67144i	1.31842	+	0.149142i
$607$	23.0516	+	39.9265i	0.935635	+	1.62057i	0.773499	+	0.633798i	$0.218505\pi$
$607$	23.0516	+	39.9265i	0.935635	+	1.62057i	0.162136	+	0.986768i	$0.448162\pi$
$608$	−0.360125	−	10.2316i	−0.0146050	−	0.414947i
$609$	35.8087	+	78.0956i	1.45104	+	3.16459i
$610$	−6.59108	−	5.67717i	−0.266865	−	0.229862i
$611$	−1.26021	+	1.84840i	−0.0509828	+	0.0747781i
$612$	83.4766	−	6.18126i	3.37434	−	0.249863i
$613$	−29.9313	+	32.2583i	−1.20891	+	1.30290i	−0.268335	+	0.963326i	$0.586474\pi$
$613$	−29.9313	+	32.2583i	−1.20891	+	1.30290i	−0.940579	+	0.339574i	$0.889717\pi$
$614$	−12.9300	−	2.45243i	−0.521814	−	0.0989722i
$615$	10.4936	−	5.05343i	0.423141	−	0.203774i
$616$	−9.25101	−	9.63270i	−0.372734	−	0.388113i
$617$	5.41139	+	2.60599i	0.217855	+	0.104913i	0.539628	−	0.841903i	$-0.318565\pi$
$617$	5.41139	+	2.60599i	0.217855	+	0.104913i	−0.321774	+	0.946817i	$0.604279\pi$
$618$	−23.5953	−	17.4303i	−0.949142	−	0.701149i
$619$	−5.06967	−	2.92697i	−0.203767	−	0.117645i	0.394644	−	0.918834i	$-0.370868\pi$
$619$	−5.06967	−	2.92697i	−0.203767	−	0.117645i	−0.598411	+	0.801189i	$0.704201\pi$
$620$	−6.28401	−	0.952863i	−0.252372	−	0.0382679i
$621$	−6.36418	+	42.2236i	−0.255386	+	1.69437i
$622$	−23.3276	+	4.40310i	−0.935350	+	0.176548i
$623$	15.9058	+	9.58805i	0.637251	+	0.384137i
$624$	3.49499	−	1.07128i	0.139912	−	0.0428854i
$625$	1.43187	+	19.1069i	0.0572746	+	0.764277i
$626$	−1.96527	−	17.5120i	−0.0785480	−	0.699922i
$627$	−10.1334	+	3.97708i	−0.404690	+	0.158829i
$628$	−26.4397	−	12.7616i	−1.05506	−	0.509243i
$629$	−1.81768	+	1.44955i	−0.0724756	+	0.0577974i
$630$	4.74906	+	19.2003i	0.189207	+	0.764957i
$631$	−11.1987	+	14.0427i	−0.445811	+	0.559030i	−0.953064	−	0.302767i	$-0.902089\pi$
$631$	−11.1987	+	14.0427i	−0.445811	+	0.559030i	0.507253	+	0.861797i	$0.330661\pi$
$632$	25.3104	−	29.3321i	1.00679	−	1.16677i
$633$	−0.788795	+	10.5257i	−0.0313518	+	0.418360i
$634$	−22.3441	+	14.0259i	−0.887398	+	0.557040i
$635$	3.87447	+	4.17568i	0.153754	+	0.165707i
$636$	1.09151	−	1.17427i	0.0432811	−	0.0465630i
$637$	−0.211845	−	1.88626i	−0.00839359	−	0.0747363i
$638$	9.71488	+	22.2937i	0.384616	+	0.882616i
$639$	70.2085	−	65.1440i	2.77741	−	2.57706i
$640$	−7.10760	−	0.823184i	−0.280952	−	0.0325392i
$641$	2.00429	−	26.7453i	0.0791646	−	1.05638i	−0.806250	−	0.591575i	$-0.798506\pi$
$641$	2.00429	−	26.7453i	0.0791646	−	1.05638i	0.885414	−	0.464802i	$-0.153875\pi$
$642$	76.4636	−	2.82711i	3.01778	−	0.111577i
$643$	−7.08244	−	5.64806i	−0.279304	−	0.222738i	0.473811	−	0.880627i	$-0.342878\pi$
$643$	−7.08244	−	5.64806i	−0.279304	−	0.222738i	−0.753115	+	0.657889i	$0.771450\pi$
$644$	−7.99265	+	9.62584i	−0.314954	+	0.379311i
$645$	12.9027	−	10.2895i	0.508041	−	0.405150i
$646$	9.71780	−	8.35535i	0.382342	−	0.328737i
$647$	−9.75785	−	24.8626i	−0.383621	−	0.977449i	−0.984069	−	0.177786i	$-0.943107\pi$
$647$	−9.75785	−	24.8626i	−0.383621	−	0.977449i	0.600449	−	0.799663i	$-0.294989\pi$
$648$	−81.3656	−	60.2179i	−3.19634	−	2.36558i
$649$	−1.40603	−	18.7621i	−0.0551914	−	0.736478i
$650$	−1.04688	−	1.41978i	−0.0410619	−	0.0556885i
$651$	−15.5793	−	42.0108i	−0.610602	−	1.64653i
$652$	−6.63459	+	4.51477i	−0.259830	+	0.176812i
$653$	−3.69699	+	24.5279i	−0.144674	+	0.959851i	0.792219	+	0.610237i	$0.208926\pi$
$653$	−3.69699	+	24.5279i	−0.144674	+	0.959851i	−0.936894	+	0.349615i	$0.886312\pi$
$654$	3.73666	+	2.35021i	0.146115	+	0.0919004i
$655$	2.10248	−	3.64160i	0.0821505	−	0.142289i
$656$	−18.0814	+	12.2807i	−0.705959	+	0.479483i
$657$	−20.0459	−	9.65359i	−0.782065	−	0.376622i
$658$	27.0083	+	14.9489i	1.05289	+	0.582770i
$659$	6.39948	+	13.2887i	0.249288	+	0.517652i	0.987635	−	0.156768i	$-0.0501076\pi$
$659$	6.39948	+	13.2887i	0.249288	+	0.517652i	−0.738347	+	0.674421i	$0.764393\pi$
$660$	1.68635	+	7.41871i	0.0656411	+	0.288773i
$661$	−0.0508902	+	0.0548466i	−0.00197940	+	0.00213329i	−0.734041	−	0.679105i	$-0.762368\pi$
$661$	−0.0508902	+	0.0548466i	−0.00197940	+	0.00213329i	0.732061	+	0.681239i	$0.238558\pi$
$662$	−24.7927	−	8.68770i	−0.963598	−	0.337657i
$663$	3.78082	+	2.57772i	0.146835	+	0.100110i
$664$	2.26986	+	20.3893i	0.0880876	+	0.791258i
$665$	2.33155	+	1.93247i	0.0904138	+	0.0749381i
$666$	5.48452	+	0.207652i	0.212521	+	0.00804635i
$667$	19.7296	−	11.3909i	0.763932	−	0.441056i
$668$	−9.70897	−	31.5751i	−0.375651	−	1.22168i
$669$	−6.40690	−	9.39719i	−0.247705	−	0.363317i
$670$	1.46517	+	5.47780i	0.0566045	+	0.211626i
$671$	3.86261	−	16.9232i	0.149114	−	0.653313i
$672$	−19.1912	−	46.6476i	−0.740317	−	1.79947i
$673$	−0.280711	−	1.22987i	−0.0108206	−	0.0474082i	0.969229	−	0.246159i	$-0.0791686\pi$
$673$	−0.280711	−	1.22987i	−0.0108206	−	0.0474082i	−0.980050	+	0.198751i	$0.936311\pi$
$674$	−9.86126	+	5.20623i	−0.379841	+	0.200537i
$675$	−24.4863	+	79.3826i	−0.942477	+	3.05544i
$676$	−24.0574	−	9.46648i	−0.925286	−	0.364095i
$677$	2.62411	+	8.50715i	0.100853	+	0.326956i	0.991911	−	0.126932i	$-0.0405129\pi$
$677$	2.62411	+	8.50715i	0.100853	+	0.326956i	−0.891059	+	0.453888i	$0.850037\pi$
$678$	−37.3332	−	19.7523i	−1.43377	−	0.758584i
$679$	3.08551	+	3.45394i	0.118411	+	0.132550i
$680$	−4.75520	−	7.59026i	−0.182354	−	0.291073i
$681$	−9.87876	+	25.1707i	−0.378555	+	0.964542i
$682$	−4.18355	−	11.9729i	−0.160196	−	0.458467i
$683$	3.14926	+	20.8940i	0.120503	+	0.799486i	0.964681	+	0.263422i	$0.0848512\pi$
$683$	3.14926	+	20.8940i	0.120503	+	0.799486i	−0.844178	+	0.536064i	$0.819911\pi$
$684$	−30.2548	−	0.0268325i	−1.15682	−	0.00102597i
$685$			0.731005i			0.0279303i
$686$	−25.6447	+	5.32451i	−0.979118	+	0.203291i
$687$	87.0726			3.32203
$688$	−21.1058	+	22.6659i	−0.804653	+	0.864130i
$689$	0.0637750	−	0.00961253i	0.00242963	−	0.000366208i
$690$	6.72828	−	2.35098i	0.256141	−	0.0895003i
$691$	−37.9784	−	14.9054i	−1.44477	−	0.567030i	−0.491964	−	0.870616i	$-0.663721\pi$
$691$	−37.9784	−	14.9054i	−1.44477	−	0.567030i	−0.952804	+	0.303586i	$0.901816\pi$
$692$	6.45515	−	0.967104i	0.245388	−	0.0367638i
$693$	−29.4336	+	26.2939i	−1.11809	+	0.998824i
$694$	0.443896	+	0.234858i	0.0168500	+	0.00891507i
$695$	−11.1299	+	3.43313i	−0.422182	+	0.130226i
$696$	3.31212	+	91.7860i	0.125546	+	3.47914i
$697$	−26.1458	−	8.06490i	−0.990341	−	0.305480i
$698$	11.1267	+	21.0753i	0.421151	+	0.797712i
$699$	−52.7827	+	12.0473i	−1.99643	+	0.455671i
$700$	−18.1670	+	16.2002i	−0.686649	+	0.612312i
$701$	−19.6651	−	4.48843i	−0.742740	−	0.169526i	−0.165625	−	0.986189i	$-0.552964\pi$
$701$	−19.6651	−	4.48843i	−0.742740	−	0.169526i	−0.577115	+	0.816663i	$0.695821\pi$
$702$	−1.78944	−	6.69015i	−0.0675381	−	0.252504i
$703$	0.694308	−	0.473371i	0.0261863	−	0.0178535i
$704$	−5.18084	−	13.3045i	−0.195260	−	0.501433i
$705$	−8.79235	−	15.2288i	−0.331139	−	0.573550i
$706$	1.43415	−	37.8790i	0.0539750	−	1.42559i
$707$	11.5702	−	13.9595i	0.435141	−	0.525002i
$708$	21.0053	−	67.8838i	0.789428	−	2.55123i
$709$	−3.29337	+	4.83048i	−0.123685	+	0.181413i	−0.883087	−	0.469209i	$-0.844539\pi$
$709$	−3.29337	+	4.83048i	−0.123685	+	0.181413i	0.759402	+	0.650621i	$0.225492\pi$
$710$	−9.67176	−	3.38911i	−0.362975	−	0.127191i
$711$	−83.9276	−	77.8735i	−3.14753	−	2.92048i
$712$	11.7687	+	15.9905i	0.441051	+	0.599270i
$713$	−10.7047	+	5.15511i	−0.400894	+	0.193060i
$714$	30.5775	−	55.2445i	1.14433	−	2.06747i
$715$	−0.132794	+	0.275749i	−0.00496620	+	0.0103124i
$716$	2.50727	−	10.9403i	0.0937012	−	0.408860i
$717$	76.6045	+	44.2276i	2.86085	+	1.65171i
$718$	3.28796	+	2.06800i	0.122706	+	0.0771770i
$719$	−5.81694	−	0.876763i	−0.216935	−	0.0326977i	0.0396753	−	0.999213i	$-0.487368\pi$
$719$	−5.81694	−	0.876763i	−0.216935	−	0.0326977i	−0.256610	+	0.966515i	$0.582606\pi$
$720$	−3.18851	+	20.9027i	−0.118829	+	0.778999i
$721$	−15.2680	+	5.66201i	−0.568611	+	0.210864i
$722$	17.8983	−	13.1973i	0.666107	−	0.491154i
$723$	−34.5255	+	2.58733i	−1.28402	+	0.0962238i
$724$	−7.86578	−	13.6519i	−0.292329	−	0.507368i
$725$	41.2578	−	16.1925i	1.53228	−	0.601374i
$726$	28.2431	−	24.2834i	1.04820	−	0.901240i
$727$	−19.5548	−	24.5209i	−0.725247	−	0.909431i	0.273375	−	0.961907i	$-0.411860\pi$
$727$	−19.5548	−	24.5209i	−0.725247	−	0.909431i	−0.998622	+	0.0524766i	$0.983289\pi$
$728$	0.564691	−	1.94902i	0.0209288	−	0.0722354i
$729$	−72.6650	+	91.1190i	−2.69130	+	3.37478i
$730$	0.0879644	+	2.37913i	0.00325571	+	0.0880556i
$731$	−38.6611	−	2.89725i	−1.42993	−	0.107159i
$732$	36.9788	−	54.1347i	1.36678	−	2.00088i
$733$	−19.6521	−	21.1800i	−0.725868	−	0.782300i	0.257039	−	0.966401i	$-0.417253\pi$
$733$	−19.6521	−	21.1800i	−0.725868	−	0.782300i	−0.982907	+	0.184101i	$0.941063\pi$
$734$	10.9460	+	25.1188i	0.404023	+	0.927153i
$735$	14.0810	+	4.93282i	0.519385	+	0.181950i
$736$	−11.8392	+	6.22368i	−0.436400	+	0.229408i
$737$	−8.29443	+	7.69611i	−0.305529	+	0.283490i
$738$	34.3411	+	54.7074i	1.26411	+	2.01381i
$739$	13.4246	+	1.00603i	0.493831	+	0.0370075i	0.319319	−	0.947647i	$-0.396546\pi$
$739$	13.4246	+	1.00603i	0.493831	+	0.0370075i	0.174513	+	0.984655i	$0.444165\pi$
$740$	−0.254344	−	0.529352i	−0.00934989	−	0.0194594i
$741$	−1.29311	−	1.03122i	−0.0475037	−	0.0378830i
$742$	−0.213684	−	0.863918i	−0.00784459	−	0.0317154i
$743$	6.23830	+	7.82258i	0.228861	+	0.286983i	0.882982	−	0.469408i	$-0.155533\pi$
$743$	6.23830	+	7.82258i	0.228861	+	0.286983i	−0.654121	+	0.756390i	$0.726961\pi$
$744$	1.85472	−	47.8642i	0.0679974	−	1.75479i
$745$	−3.23876	−	8.25223i	−0.118659	−	0.302338i
$746$	28.4252	−	3.18998i	1.04072	−	0.116794i
$747$	60.4564	−	4.53058i	2.21199	−	0.165765i
$748$	8.95013	−	15.4704i	0.327249	−	0.565653i
$749$	21.9277	−	36.3763i	0.801222	−	1.32916i
$750$	28.4353	−	5.36718i	1.03831	−	0.195982i
$751$	−29.0433	−	4.37757i	−1.05980	−	0.159740i	−0.404067	−	0.914729i	$-0.632404\pi$
$751$	−29.0433	−	4.37757i	−1.05980	−	0.159740i	−0.655737	+	0.754989i	$0.727642\pi$
$752$	20.5298	+	25.8375i	0.748646	+	0.942196i
$753$	−37.1618	+	64.3661i	−1.35425	+	2.34563i
$754$	−2.19538	+	2.97188i	−0.0799512	+	0.108229i
$755$	4.58138	−	9.51333i	0.166733	−	0.346225i
$756$	−89.6276	+	33.1472i	−3.25972	+	1.20555i
$757$	21.7706	+	45.2071i	0.791265	+	1.64308i	0.765521	+	0.643411i	$0.222481\pi$
$757$	21.7706	+	45.2071i	0.791265	+	1.64308i	0.0257445	+	0.999669i	$0.491804\pi$
$758$	33.3528	+	6.32601i	1.21143	+	0.229771i
$759$	10.4254	+	9.67339i	0.378419	+	0.351122i
$760$	1.50892	+	2.86423i	0.0547343	+	0.103897i
$761$	34.1253	+	23.2662i	1.23704	+	0.843400i	0.992015	−	0.126117i	$-0.0402514\pi$
$761$	34.1253	+	23.2662i	1.23704	+	0.843400i	0.245025	+	0.969517i	$0.421204\pi$
$762$	−28.0168	+	32.5270i	−1.01494	+	1.17833i
$763$	2.22741	−	1.02132i	0.0806376	−	0.0369743i
$764$	32.2360	−	12.6187i	1.16626	−	0.456530i
$765$	−22.9226	+	13.2344i	−0.828769	+	0.478490i
$766$	−14.5839	−	1.64976i	−0.526938	−	0.0596083i
$767$	2.36190	−	1.61032i	0.0852834	−	0.0581452i
$768$	0.191296	−	53.9234i	0.00690279	−	1.94579i
$769$	−1.65125	+	7.23460i	−0.0595456	+	0.260886i	−0.995935	−	0.0900770i	$-0.971289\pi$
$769$	−1.65125	+	7.23460i	−0.0595456	+	0.260886i	0.936389	+	0.350963i	$0.114146\pi$
$770$	3.95852	+	1.47160i	0.142655	+	0.0530327i
$771$	44.1091	−	10.0676i	1.58855	−	0.362576i
$772$	−13.0308	−	10.4107i	−0.468990	−	0.374688i
$773$	−9.82945	+	31.8663i	−0.353541	+	1.14615i	0.587889	+	0.808942i	$0.299959\pi$
$773$	−9.82945	+	31.8663i	−0.353541	+	1.14615i	−0.941430	+	0.337209i	$0.890517\pi$
$774$	64.6887	+	64.7461i	2.32519	+	2.32725i
$775$	−22.0880	+	6.81326i	−0.793426	+	0.244739i
$776$	1.62906	+	4.67552i	0.0584798	+	0.167842i
$777$	2.39640	−	3.37612i	0.0859703	−	0.121118i
$778$	5.59164	−	20.8313i	0.200470	−	0.746839i
$779$	9.20600	+	3.61309i	0.329839	+	0.129452i
$780$	−0.848044	+	0.785471i	−0.0303648	+	0.0281244i
$781$	−3.04793	−	20.2217i	−0.109063	−	0.723589i
$782$	−15.3434	−	6.70235i	−0.548678	−	0.239676i
$783$	174.002			6.21833
$784$	−27.5007	−	5.26419i	−0.982168	−	0.188007i
$785$	9.28355			0.331344
$786$	29.0404	+	12.6855i	1.03584	+	0.452478i
$787$	−0.701906	−	4.65684i	−0.0250203	−	0.165999i	0.972831	−	0.231516i	$-0.0743684\pi$
$787$	−0.701906	−	4.65684i	−0.0250203	−	0.165999i	−0.997851	+	0.0655170i	$0.979130\pi$
$788$	9.85575	−	9.12855i	0.351097	−	0.325191i
$789$	7.23942	+	2.84126i	0.257730	+	0.101152i
$790$	−3.17603	+	11.8321i	−0.112998	+	0.420967i
$791$	−20.5222	+	11.3374i	−0.729685	+	0.403112i
$792$	−39.8436	+	13.8824i	−1.41578	+	0.493290i
$793$	2.52018	−	0.777374i	0.0894944	−	0.0276054i
$794$	−4.21505	−	4.21879i	−0.149586	−	0.149719i
$795$	−0.149429	+	0.484437i	−0.00529971	+	0.0171812i
$796$	34.4253	+	27.5033i	1.22017	+	0.974827i
$797$	−6.70826	+	1.53112i	−0.237619	+	0.0542349i	−0.339672	−	0.940544i	$-0.610316\pi$
$797$	−6.70826	+	1.53112i	−0.237619	+	0.0542349i	0.102053	+	0.994779i	$0.467459\pi$
$798$	−12.5134	+	19.0861i	−0.442969	+	0.675641i
$799$	−9.19244	+	40.2747i	−0.325205	+	1.42482i
$800$	−24.5805	+	8.53995i	−0.869051	+	0.301933i
$801$	48.4780	−	33.0517i	1.71289	−	1.16783i
$802$	−7.45364	−	0.843170i	−0.263197	−	0.0297734i
$803$	−4.11421	+	2.37534i	−0.145187	+	0.0838240i
$804$	−39.7939	+	15.5772i	−1.40342	+	0.549367i
$805$	0.953026	−	3.83983i	0.0335898	−	0.135336i
$806$	1.25758	−	1.46002i	0.0442963	−	0.0514271i
$807$	−55.7429	−	38.0049i	−1.96224	−	1.33783i
$808$	17.1488	−	9.03425i	0.603293	−	0.317824i
$809$	6.98374	+	6.47996i	0.245535	+	0.227823i	0.793334	−	0.608787i	$-0.208344\pi$
$809$	6.98374	+	6.47996i	0.245535	+	0.227823i	−0.547799	+	0.836610i	$0.684534\pi$
$810$	31.4482	+	5.96477i	1.10498	+	0.209581i
$811$	18.4404	+	38.2920i	0.647532	+	1.34461i	0.923556	+	0.383463i	$0.125269\pi$
$811$	18.4404	+	38.2920i	0.647532	+	1.34461i	−0.276025	+	0.961151i	$0.589017\pi$
$812$	43.6409	+	26.3597i	1.53150	+	0.925043i
$813$	18.5584	−	38.5370i	0.650873	−	1.35155i
$814$	0.696316	−	0.942599i	0.0244059	−	0.0330381i
$815$	1.26881	−	2.19765i	0.0444445	−	0.0769802i
$816$	52.8496	−	41.9930i	1.85011	−	1.47005i
$817$	13.8566	+	2.08854i	0.484780	+	0.0730688i
$818$	−48.4856	+	9.15169i	−1.69526	+	0.319981i
$819$	−5.69574	−	1.87537i	−0.199025	−	0.0655308i
$820$	3.46114	−	5.98261i	0.120868	−	0.208922i
$821$	11.9481	−	0.895388i	0.416992	−	0.0312493i	0.135418	−	0.990789i	$-0.456762\pi$
$821$	11.9481	−	0.895388i	0.416992	−	0.0312493i	0.281575	+	0.959539i	$0.409143\pi$
$822$	−5.47478	+	0.614401i	−0.190955	+	0.0214297i
$823$	9.94173	+	25.3311i	0.346547	+	0.882987i	0.992791	+	0.119857i	$0.0382435\pi$
$823$	9.94173	+	25.3311i	0.346547	+	0.882987i	−0.646244	+	0.763131i	$0.723661\pi$
$824$	−17.3953	−	0.674063i	−0.605995	−	0.0234821i
$825$	17.2511	+	21.6322i	0.600607	+	0.753137i
$826$	−25.1472	−	30.3900i	−0.874983	−	1.05740i
$827$	−37.2759	−	29.7266i	−1.29621	−	1.03369i	−0.996830	−	0.0795606i	$-0.974648\pi$
$827$	−37.2759	−	29.7266i	−1.29621	−	1.03369i	−0.299381	−	0.954134i	$-0.596780\pi$
$828$	17.1183	+	35.6274i	0.594904	+	1.23814i
$829$	−11.5846	−	0.868147i	−0.402350	−	0.0301520i	−0.127982	−	0.991777i	$-0.540850\pi$
$829$	−11.5846	−	0.868147i	−0.402350	−	0.0301520i	−0.274369	+	0.961625i	$0.588469\pi$
$830$	−3.44897	−	5.49441i	−0.119716	−	0.190714i
$831$	22.0993	−	20.5052i	0.766616	−	0.711316i
$832$	1.35703	−	1.69241i	0.0470466	−	0.0586736i
$833$	−16.3669	−	30.9945i	−0.567078	−	1.07390i
$834$	−35.0666	−	80.4708i	−1.21426	−	2.78648i
$835$	7.10498	+	7.65735i	0.245878	+	0.264993i
$836$	−3.64381	+	5.33431i	−0.126024	+	0.184491i
$837$	−90.4933	−	6.78154i	−3.12791	−	0.234404i
$838$	1.67688	+	45.3538i	0.0579268	+	1.56672i
$839$	−2.53004	+	3.17257i	−0.0873466	+	0.109529i	−0.823584	−	0.567194i	$-0.808029\pi$
$839$	−2.53004	+	3.17257i	−0.0873466	+	0.109529i	0.736238	+	0.676723i	$0.236600\pi$
$840$	11.8771	+	10.6463i	0.409797	+	0.367332i
$841$	−39.8001	−	49.9077i	−1.37242	−	1.72095i
$842$	27.2119	−	23.3967i	0.937784	−	0.806304i
$843$	17.7692	−	6.97389i	0.612003	−	0.240194i
$844$	3.12709	+	5.42740i	0.107639	+	0.186819i
$845$	8.15221	−	0.610923i	0.280444	−	0.0210164i
$846$	78.4922	−	57.8761i	2.69862	−	1.98982i
$847$	−2.69509	−	20.4997i	−0.0926043	−	0.704377i
$848$	0.143467	−	0.940520i	0.00492668	−	0.0322976i
$849$	8.94332	+	1.34799i	0.306934	+	0.0462629i
$850$	−27.5736	−	17.3427i	−0.945765	−	0.594849i
$851$	−0.950761	−	0.548922i	−0.0325917	−	0.0188168i
$852$	17.2533	−	75.2840i	0.591090	−	2.57919i
$853$	−13.1327	+	27.2702i	−0.449654	+	0.933715i	0.545750	+	0.837948i	$0.316245\pi$
$853$	−13.1327	+	27.2702i	−0.449654	+	0.933715i	−0.995404	+	0.0957673i	$0.969470\pi$
$854$	−13.9057	−	33.6306i	−0.475844	−	1.15082i
$855$	8.61958	−	4.15097i	0.294783	−	0.141960i
$856$	36.5701	−	26.9149i	1.24994	−	0.919932i
$857$	−7.35887	−	6.82803i	−0.251374	−	0.233241i	0.544413	−	0.838817i	$-0.316752\pi$
$857$	−7.35887	−	6.82803i	−0.251374	−	0.233241i	−0.795788	+	0.605576i	$0.792943\pi$
$858$	−2.17680	−	0.762778i	−0.0743147	−	0.0260408i
$859$	8.11278	−	11.8993i	0.276805	−	0.405998i	−0.662511	−	0.749052i	$-0.730509\pi$
$859$	8.11278	−	11.8993i	0.276805	−	0.405998i	0.939316	+	0.343054i	$0.111462\pi$
$860$	2.89497	−	9.35580i	0.0987177	−	0.319030i
$861$	48.7162	+	0.919844i	1.66024	+	0.0313482i
$862$	1.84039	−	48.6085i	0.0626838	−	1.65561i
$863$	−9.91740	−	17.1774i	−0.337592	−	0.584727i	0.646387	−	0.763010i	$-0.276279\pi$
$863$	−9.91740	−	17.1774i	−0.337592	−	0.584727i	−0.983979	+	0.178283i	$0.942946\pi$
$864$	−102.079	−	4.04617i	−3.47278	−	0.137654i
$865$	−1.70535	+	1.16269i	−0.0579836	+	0.0395326i
$866$	0.447042	+	1.67135i	0.0151911	+	0.0567947i
$867$	26.5229	+	6.05368i	0.900765	+	0.205594i
$868$	−21.6690	−	15.4097i	−0.735493	−	0.523040i
$869$	−23.8333	+	5.43979i	−0.808488	+	0.184532i
$870$	−13.5595	−	25.6833i	−0.459709	−	0.870746i
$871$	−1.64276	−	0.506724i	−0.0556628	−	0.0171697i
$872$	2.61788	−	0.0944669i	0.0886526	−	0.00319905i
$873$	13.9816	−	4.31274i	0.473204	−	0.145964i
$874$	5.34925	+	2.83020i	0.180941	+	0.0957329i
$875$	6.14980	−	14.8394i	0.207901	−	0.501663i
$876$	−17.7443	+	2.65843i	−0.599524	+	0.0898200i
$877$	37.5218	+	14.7262i	1.26702	+	0.497269i	0.901195	−	0.433415i	$-0.142692\pi$
$877$	37.5218	+	14.7262i	1.26702	+	0.497269i	0.365825	+	0.930684i	$0.380787\pi$
$878$	34.2708	−	11.9748i	1.15658	−	0.404130i
$879$	3.78784	−	0.570925i	0.127761	−	0.0192568i
$880$	3.30413	+	3.07671i	0.111382	+	0.103716i
$881$	−40.9146			−1.37845			−0.689224	−	0.724548i	$-0.742048\pi$
$881$	−40.9146			−1.37845			−0.689224	+	0.724548i	$0.742048\pi$
$882$	−18.4771	+	80.6552i	−0.622157	+	2.71580i
$883$			30.3912i			1.02275i	0.859359	+	0.511373i	$0.170863\pi$
$883$			30.3912i			1.02275i	−0.859359	+	0.511373i	$0.829137\pi$
$884$	2.71551	+	0.00240834i	0.0913324	+	8.10012e-5i
$885$	3.34897	+	22.2190i	0.112575	+	0.746883i
$886$	13.7230	+	39.2739i	0.461033	+	1.31943i
$887$	8.97002	−	22.8552i	0.301184	−	0.767404i	−0.697523	−	0.716562i	$-0.745714\pi$
$887$	8.97002	−	22.8552i	0.301184	−	0.767404i	0.998707	−	0.0508414i	$-0.0161903\pi$
$888$	3.75075	−	2.34980i	0.125867	−	0.0788540i
$889$	6.59298	+	22.9002i	0.221121	+	0.768048i
$890$	−5.54940	−	2.93609i	−0.186016	−	0.0984180i
$891$	18.8266	+	61.0345i	0.630716	+	2.04473i
$892$	−6.28062	−	2.47139i	−0.210291	−	0.0827483i
$893$	4.40113	−	14.2681i	0.147278	−	0.477464i
$894$	59.0819	−	31.1922i	1.97600	−	1.04322i
$895$	0.789766	+	3.46019i	0.0263990	+	0.115661i
$896$	−24.9890	−	16.4787i	−0.834825	−	0.550516i
$897$	−0.480827	+	2.10664i	−0.0160543	+	0.0703386i
$898$	9.92435	+	37.1040i	0.331180	+	1.23818i
$899$	27.2736	+	40.0030i	0.909624	+	1.33417i
$900$	22.6010	+	73.5022i	0.753368	+	2.45007i
$901$	1.03140	−	0.595482i	0.0343611	−	0.0198384i
$902$	13.7820	+	0.521807i	0.458891	+	0.0173743i
$903$	67.5875	−	14.0895i	2.24917	−	0.468870i
$904$	−24.9105	+	2.77319i	−0.828512	+	0.0922349i
$905$	4.11648	+	2.80657i	0.136837	+	0.0932936i
$906$	75.0995	+	26.3158i	2.49501	+	0.874285i
$907$	−1.56877	+	1.69073i	−0.0520902	+	0.0561399i	−0.758559	−	0.651604i	$-0.774096\pi$
$907$	−1.56877	+	1.69073i	−0.0520902	+	0.0561399i	0.706469	+	0.707744i	$0.250287\pi$
$908$	3.55676	+	15.6471i	0.118035	+	0.519268i
$909$	−24.8528	−	51.6074i	−0.824316	−	1.71171i
$910$	0.107087	+	0.632654i	0.00354990	+	0.0209723i
$911$	0.183551	+	0.0883937i	0.00608133	+	0.00292861i	0.436922	−	0.899499i	$-0.356069\pi$
$911$	0.183551	+	0.0883937i	0.00608133	+	0.00292861i	−0.430841	+	0.902428i	$0.641783\pi$
$912$	−20.1831	+	13.7082i	−0.668330	+	0.453925i
$913$	6.47246	−	11.2106i	0.214207	−	0.371018i
$914$	−33.7527	−	21.2291i	−1.11644	−	0.702196i
$915$	−3.08975	+	20.4992i	−0.102144	+	0.677682i
$916$	42.7189	−	29.0698i	1.41147	−	0.960492i
$917$	14.7191	−	9.63340i	0.486069	−	0.318123i
$918$	−75.8936	−	102.928i	−2.50486	−	3.39712i
$919$	2.63428	+	35.1520i	0.0868968	+	1.15956i	0.854788	+	0.518977i	$0.173687\pi$
$919$	2.63428	+	35.1520i	0.0868968	+	1.15956i	−0.767891	+	0.640580i	$0.778694\pi$
$920$	2.51609	−	3.39970i	0.0829529	−	0.112085i
$921$	11.4582	+	29.1951i	0.377561	+	0.962011i
$922$	−12.8531	+	11.0511i	−0.423294	+	0.363947i
$923$	2.42922	−	1.93724i	0.0799587	−	0.0637650i
$924$	−7.69426	+	30.8837i	−0.253123	+	1.01600i
$925$	−1.66987	−	1.33168i	−0.0549050	−	0.0437853i
$926$	7.60591	−	0.281216i	0.249946	−	0.00924132i
$927$	−3.84447	+	51.3008i	−0.126269	+	1.68494i
$928$	32.2683	+	43.9255i	1.05926	+	1.44193i
$929$	33.2778	−	30.8773i	1.09181	−	1.01305i	0.0919579	−	0.995763i	$-0.470687\pi$
$929$	33.2778	−	30.8773i	1.09181	−	1.01305i	0.999851	−	0.0172873i	$-0.00550298\pi$
$930$	6.05089	+	13.8856i	0.198417	+	0.455326i
$931$	5.06200	+	11.6136i	0.165900	+	0.380620i
$932$	−21.8738	+	23.5324i	−0.716499	+	0.770830i
$933$	38.4800	+	41.4716i	1.25978	+	1.35772i
$934$	−9.03280	+	5.67010i	−0.295562	+	0.185531i
$935$	−0.422347	+	5.63583i	−0.0138122	+	0.184311i
$936$	−4.85347	−	4.18800i	−0.158641	−	0.136889i
$937$	9.20502	−	11.5427i	0.300715	−	0.377085i	−0.608400	−	0.793631i	$-0.708188\pi$
$937$	9.20502	−	11.5427i	0.300715	−	0.377085i	0.909115	+	0.416546i	$0.136760\pi$
$938$	−4.85970	+	23.2188i	−0.158675	+	0.758119i
$939$	−32.8332	+	26.1836i	−1.07147	+	0.854469i
$940$	−9.39787	−	4.53605i	−0.306525	−	0.147950i
$941$	−34.3754	+	13.4913i	−1.12061	+	0.439805i	−0.852051	−	0.523459i	$-0.824641\pi$
$941$	−34.3754	+	13.4913i	−1.12061	+	0.439805i	−0.268555	+	0.963264i	$0.586546\pi$
$942$	7.80271	+	69.5280i	0.254226	+	2.26535i
$943$	−0.965539	−	12.8842i	−0.0314423	−	0.419568i
$944$	−12.3580	−	40.3174i	−0.402218	−	1.31222i
$945$	20.9677	−	21.7591i	0.682080	−	0.707825i
$946$	19.2033	−	3.62464i	0.624352	−	0.117847i
$947$	1.13636	−	7.53923i	0.0369266	−	0.244992i	−0.962751	−	0.270390i	$-0.912847\pi$
$947$	1.13636	−	7.53923i	0.0369266	−	0.244992i	0.999677	+	0.0253981i	$0.00808535\pi$
$948$	−91.2846	−	13.8417i	−2.96478	−	0.449559i
$949$	−0.625093	−	0.360898i	−0.0202914	−	0.0117152i
$950$	9.47003	+	6.99569i	0.307248	+	0.226970i
$951$	56.6441	+	27.2784i	1.83681	+	0.884561i
$952$	−3.44205	−	37.3121i	−0.111558	−	1.20929i
$953$	−1.50338	+	0.723989i	−0.0486992	+	0.0234523i	−0.458075	−	0.888914i	$-0.651461\pi$
$953$	−1.50338	+	0.723989i	−0.0486992	+	0.0234523i	0.409376	+	0.912366i	$0.365747\pi$
$954$	−2.76229	−	0.523923i	−0.0894326	−	0.0169626i
$955$	−7.44561	+	8.02446i	−0.240934	+	0.259665i
$956$	52.3487	−	3.87631i	1.69308	−	0.125369i
$957$	32.6465	−	47.8836i	1.05531	−	1.54786i
$958$	−19.2614	−	16.5906i	−0.622306	−	0.536018i
$959$	−1.37866	+	2.72976i	−0.0445192	+	0.0881484i
$960$	7.35744	+	15.3824i	0.237460	+	0.496466i
$961$	2.87491	+	4.97949i	0.0927391	+	0.160629i
$962$	0.176924	+	0.0200140i	0.00570427	+	0.000645278i
$963$	−75.5889	−	110.869i	−2.43582	−	3.57269i
$964$	−16.0748	+	12.7959i	−0.517735	+	0.412129i
$965$	5.14186	+	1.17360i	0.165522	+	0.0377794i
$966$	29.5590	+	3.91025i	0.951044	+	0.125810i
$967$	1.26431	+	5.53929i	0.0406574	+	0.178132i	0.991180	−	0.132525i	$-0.0423084\pi$
$967$	1.26431	+	5.53929i	0.0406574	+	0.178132i	−0.950522	+	0.310656i	$0.899451\pi$
$968$	5.74924	−	21.3429i	0.184788	−	0.685985i
$969$	−29.1849	−	9.00234i	−0.937553	−	0.289197i
$970$	−1.10658	−	1.10756i	−0.0355302	−	0.0355617i
$971$	−9.54762	−	30.9526i	−0.306398	−	0.993317i	−0.969563	−	0.244844i	$-0.921263\pi$
$971$	−9.54762	−	30.9526i	−0.306398	−	0.993317i	0.663165	−	0.748473i	$-0.269213\pi$
$972$	−10.0473	+	132.495i	−0.322268	+	4.24979i
$973$	−48.0367	−	8.17064i	−1.53999	−	0.261939i
$974$	16.9788	+	4.55752i	0.544035	+	0.146032i
$975$	−1.53584	+	3.91324i	−0.0491861	+	0.125324i
$976$	0.0690080	−	38.9047i	0.00220889	−	1.24531i
$977$	4.28805	−	0.646320i	0.137187	−	0.0206776i	−0.0800898	−	0.996788i	$-0.525521\pi$
$977$	4.28805	−	0.646320i	0.137187	−	0.0206776i	0.217277	+	0.976110i	$0.430283\pi$
$978$	17.5254	+	7.65552i	0.560401	+	0.244797i
$979$		−	12.5279i		−	0.400395i
$980$	8.55515	−	2.28093i	0.273284	−	0.0728615i
$981$		−	7.74130i		−	0.247161i
$982$	−1.44244	+	3.30211i	−0.0460301	+	0.105375i
$983$	−22.2840	+	3.35877i	−0.710748	+	0.107128i	−0.494459	−	0.869201i	$-0.664634\pi$
$983$	−22.2840	+	3.35877i	−0.710748	+	0.107128i	−0.216290	+	0.976329i	$0.569396\pi$
$984$	47.7151	+	20.8935i	1.52110	+	0.666060i
$985$	−1.55195	+	3.95430i	−0.0494492	+	0.125995i
$986$	−17.6880	+	65.8957i	−0.563302	+	2.09855i
$987$	−4.11165	−	73.4503i	−0.130875	−	2.33795i
$988$	−0.978698	−	0.0742162i	−0.0311365	−	0.00236113i
$989$	−5.39621	−	17.4941i	−0.171589	−	0.556279i
$990$	9.43838	−	9.43001i	0.299971	−	0.299705i
$991$	−7.13440	−	2.20067i	−0.226632	−	0.0699066i	0.179360	−	0.983784i	$-0.442597\pi$
$991$	−7.13440	−	2.20067i	−0.226632	−	0.0699066i	−0.405991	+	0.913877i	$0.633074\pi$
$992$	−15.0698	−	24.1020i	−0.478468	−	0.765239i
$993$	13.9312	+	61.0367i	0.442094	+	1.93694i
$994$	−29.7250	−	30.8965i	−0.942818	−	0.979977i
$995$	−13.5839	−	3.10045i	−0.430640	−	0.0982908i
$996$	38.2509	−	30.4486i	1.21203	−	0.964802i
$997$	0.893561	+	1.31061i	0.0282994	+	0.0415075i	0.840128	−	0.542389i	$-0.182480\pi$
$997$	0.893561	+	1.31061i	0.0282994	+	0.0415075i	−0.811828	+	0.583896i	$0.801528\pi$
$998$	3.61285	−	31.9376i	0.114363	−	1.01097i
$999$	−4.19255	−	7.26172i	−0.132647	−	0.229751i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.8	✓	648
8.5	even	2	inner	392.2.z.a.109.34	yes	648
49.9	even	21	inner	392.2.z.a.205.34	yes	648
392.205	even	42	inner	392.2.z.a.205.8	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.8	✓	648	1.1	even	1	trivial
392.2.z.a.109.34	yes	648	8.5	even	2	inner
392.2.z.a.205.8	yes	648	392.205	even	42	inner
392.2.z.a.205.34	yes	648	49.9	even	21	inner

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	392.2.z.a.109.8

Level	$392$
Weight	$2$
Character	392.109
Analytic conductor	$3.130$
Analytic rank	$0$
Dimension	$648$
Inner twists	$4$