LMFDB - Embedded newform 225.2.q.a.196.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$225 = 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	225.q (of order $15$ , degree $8$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			196.2
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66247 - 1.84635i) q^{2} +(1.70628 + 0.297695i) q^{3} +(-0.436178 + 4.14996i) q^{4} +(1.32553 - 1.80083i) q^{5} +(-2.28697 - 3.64530i) q^{6} +(-0.644527 + 1.11635i) q^{7} +(4.36740 - 3.17310i) q^{8} +(2.82275 + 1.01590i) q^{9} +(-5.52861 + 0.546422i) q^{10} +(-0.343631 - 0.381641i) q^{11} +(-1.97966 + 6.95113i) q^{12} +(3.33655 - 3.70562i) q^{13} +(3.13269 - 0.665873i) q^{14} +(2.79781 - 2.67811i) q^{15} +(-4.95605 - 1.05344i) q^{16} +(5.60571 - 4.07278i) q^{17} +(-2.81702 - 6.90071i) q^{18} +(-4.21905 + 3.06532i) q^{19} +(6.89520 + 6.28636i) q^{20} +(-1.43207 + 1.71293i) q^{21} +(-0.133370 + 1.26893i) q^{22} +(-4.07593 + 0.866366i) q^{23} +(8.39660 - 4.11403i) q^{24} +(-1.48596 - 4.77409i) q^{25} -12.3888 q^{26} +(4.51397 + 2.57373i) q^{27} +(-4.35169 - 3.16169i) q^{28} +(-6.33037 + 2.81846i) q^{29} +(-9.59600 - 0.713494i) q^{30} +(-1.40416 - 0.625171i) q^{31} +(0.895838 + 1.55164i) q^{32} +(-0.472716 - 0.753482i) q^{33} +(-16.8391 - 3.57926i) q^{34} +(1.15602 + 2.64044i) q^{35} +(-5.44717 + 11.2712i) q^{36} +(2.27325 + 6.99635i) q^{37} +(12.6737 + 2.69388i) q^{38} +(6.79622 - 5.32953i) q^{39} +(0.0748925 - 12.0710i) q^{40} +(2.72638 - 3.02795i) q^{41} +(5.54346 - 0.203577i) q^{42} +(2.08364 - 3.60897i) q^{43} +(1.73368 - 1.25959i) q^{44} +(5.57110 - 3.73669i) q^{45} +(8.37572 + 6.08531i) q^{46} +(-7.35774 + 3.27588i) q^{47} +(-8.14279 - 3.27286i) q^{48} +(2.66917 + 4.62314i) q^{49} +(-6.34430 + 10.6804i) q^{50} +(10.7773 - 5.28050i) q^{51} +(13.9228 + 15.4629i) q^{52} +(2.21350 + 1.60820i) q^{53} +(-2.75230 - 12.6131i) q^{54} +(-1.14276 + 0.112945i) q^{55} +(0.727395 + 6.92070i) q^{56} +(-8.11140 + 3.97429i) q^{57} +(15.7279 + 7.00251i) q^{58} +(-2.04720 + 2.27364i) q^{59} +(9.89368 + 12.7789i) q^{60} +(4.90975 + 5.45283i) q^{61} +(1.18008 + 3.63190i) q^{62} +(-2.95344 + 2.49642i) q^{63} +(-1.75586 + 5.40400i) q^{64} +(-2.25049 - 10.9204i) q^{65} +(-0.605320 + 2.12544i) q^{66} +(-0.415400 - 0.184948i) q^{67} +(14.4568 + 25.0399i) q^{68} +(-7.21258 + 0.264873i) q^{69} +(2.95334 - 6.52406i) q^{70} +(1.33759 + 0.971819i) q^{71} +(15.5516 - 4.52004i) q^{72} +(-2.72548 + 8.38816i) q^{73} +(9.13854 - 15.8284i) q^{74} +(-1.11424 - 8.58828i) q^{75} +(-10.8807 - 18.8459i) q^{76} +(0.647525 - 0.137636i) q^{77} +(-21.1387 - 3.68808i) q^{78} +(-3.14525 + 1.40036i) q^{79} +(-8.46644 + 7.52863i) q^{80} +(6.93589 + 5.73528i) q^{81} -10.1232 q^{82} +(-1.53461 - 14.6009i) q^{83} +(-6.48396 - 6.69019i) q^{84} +(0.0961272 - 15.4935i) q^{85} +(-10.1274 + 2.15265i) q^{86} +(-11.6404 + 2.92455i) q^{87} +(-2.71176 - 0.576402i) q^{88} +(-2.98202 + 9.17771i) q^{89} +(-16.1610 - 4.07410i) q^{90} +(1.98628 + 6.11314i) q^{91} +(-1.81755 - 17.2928i) q^{92} +(-2.20977 - 1.48473i) q^{93} +(18.2804 + 8.13897i) q^{94} +(-0.0723487 + 11.6610i) q^{95} +(1.06663 + 2.91421i) q^{96} +(7.36689 - 3.27995i) q^{97} +(4.09855 - 12.6140i) q^{98} +(-0.582277 - 1.42637i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100})$ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.66247	−	1.84635i	−1.17554	−	1.30557i	−0.942926	−	0.333001i	$-0.891939\pi$
$2$	−1.66247	−	1.84635i	−1.17554	−	1.30557i	−0.232614	−	0.972569i	$-0.574728\pi$
$3$	1.70628	+	0.297695i	0.985119	+	0.171875i
$3$	1.70628	+	0.297695i	0.985119	+	0.171875i
$4$	−0.436178	+	4.14996i	−0.218089	+	2.07498i
$5$	1.32553	−	1.80083i	0.592793	−	0.805355i
$5$	1.32553	−	1.80083i	0.592793	−	0.805355i
$6$	−2.28697	−	3.64530i	−0.933653	−	1.48819i
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	−0.961739	−	0.273966i	$-0.911664\pi$
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	0.718131	+	0.695908i	$0.244998\pi$
$8$	4.36740	−	3.17310i	1.54411	−	1.12186i
$9$	2.82275	+	1.01590i	0.940918	+	0.338634i
$10$	−5.52861	+	0.546422i	−1.74830	+	0.172794i
$11$	−0.343631	−	0.381641i	−0.103609	−	0.115069i	0.689110	−	0.724657i	$-0.258002\pi$
$11$	−0.343631	−	0.381641i	−0.103609	−	0.115069i	−0.792719	+	0.609588i	$0.791335\pi$
$12$	−1.97966	+	6.95113i	−0.571480	+	2.00662i
$13$	3.33655	−	3.70562i	0.925393	−	1.02775i	−0.0741418	−	0.997248i	$-0.523622\pi$
$13$	3.33655	−	3.70562i	0.925393	−	1.02775i	0.999535	−	0.0305051i	$-0.00971158\pi$
$14$	3.13269	−	0.665873i	0.837246	−	0.177962i
$15$	2.79781	−	2.67811i	0.722392	−	0.691484i
$16$	−4.95605	−	1.05344i	−1.23901	−	0.263360i
$17$	5.60571	−	4.07278i	1.35958	−	0.987795i	0.361113	−	0.932522i	$-0.382397\pi$
$17$	5.60571	−	4.07278i	1.35958	−	0.987795i	0.998471	−	0.0552732i	$-0.0176030\pi$
$18$	−2.81702	−	6.90071i	−0.663978	−	1.62651i
$19$	−4.21905	+	3.06532i	−0.967917	+	0.703233i	−0.954976	−	0.296683i	$-0.904119\pi$
$19$	−4.21905	+	3.06532i	−0.967917	+	0.703233i	−0.0129412	+	0.999916i	$0.504119\pi$
$20$	6.89520	+	6.28636i	1.54181	+	1.40567i
$21$	−1.43207	+	1.71293i	−0.312504	+	0.373793i
$22$	−0.133370	+	1.26893i	−0.0284345	+	0.270537i
$23$	−4.07593	+	0.866366i	−0.849891	+	0.180650i	−0.612212	−	0.790694i	$-0.709720\pi$
$23$	−4.07593	+	0.866366i	−0.849891	+	0.180650i	−0.237679	+	0.971344i	$0.576387\pi$
$24$	8.39660	−	4.11403i	1.71395	−	0.839773i
$25$	−1.48596	−	4.77409i	−0.297192	−	0.954818i
$26$	−12.3888			−2.42964
$27$	4.51397	+	2.57373i	0.868714	+	0.495314i
$28$	−4.35169	−	3.16169i	−0.822392	−	0.597503i
$29$	−6.33037	+	2.81846i	−1.17552	+	0.523375i	−0.899135	−	0.437672i	$-0.855803\pi$
$29$	−6.33037	+	2.81846i	−1.17552	+	0.523375i	−0.276385	+	0.961047i	$0.589137\pi$
$30$	−9.59600	−	0.713494i	−1.75198	−	0.130266i
$31$	−1.40416	−	0.625171i	−0.252194	−	0.112284i	0.276746	−	0.960943i	$-0.410744\pi$
$31$	−1.40416	−	0.625171i	−0.252194	−	0.112284i	−0.528940	+	0.848659i	$0.677410\pi$
$32$	0.895838	+	1.55164i	0.158363	+	0.274293i
$33$	−0.472716	−	0.753482i	−0.0822894	−	0.131164i
$34$	−16.8391	−	3.57926i	−2.88788	−	0.613838i
$35$	1.15602	+	2.64044i	0.195403	+	0.446315i
$36$	−5.44717	+	11.2712i	−0.907862	+	1.87853i
$37$	2.27325	+	6.99635i	0.373720	+	1.15019i	0.944338	+	0.328977i	$0.106704\pi$
$37$	2.27325	+	6.99635i	0.373720	+	1.15019i	−0.570618	+	0.821216i	$0.693296\pi$
$38$	12.6737	+	2.69388i	2.05595	+	0.437005i
$39$	6.79622	−	5.32953i	1.08827	−	0.853407i
$40$	0.0748925	−	12.0710i	0.0118416	−	1.90859i
$41$	2.72638	−	3.02795i	0.425789	−	0.472886i	−0.491633	−	0.870802i	$-0.663600\pi$
$41$	2.72638	−	3.02795i	0.425789	−	0.472886i	0.917422	+	0.397916i	$0.130267\pi$
$42$	5.54346	−	0.203577i	0.855374	−	0.0314126i
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	−0.662267	−	0.749268i	$-0.730405\pi$
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	0.980019	+	0.198906i	$0.0637387\pi$
$44$	1.73368	−	1.25959i	0.261362	−	0.189890i
$45$	5.57110	−	3.73669i	0.830490	−	0.557033i
$46$	8.37572	+	6.08531i	1.23493	+	0.897231i
$47$	−7.35774	+	3.27588i	−1.07324	+	0.477836i	−0.865789	−	0.500410i	$-0.833183\pi$
$47$	−7.35774	+	3.27588i	−1.07324	+	0.477836i	−0.207449	+	0.978246i	$0.566516\pi$
$48$	−8.14279	−	3.27286i	−1.17531	−	0.472396i
$49$	2.66917	+	4.62314i	0.381310	+	0.660448i
$50$	−6.34430	+	10.6804i	−0.897220	+	1.51043i
$51$	10.7773	−	5.28050i	1.50913	−	0.739418i
$52$	13.9228	+	15.4629i	1.93075	+	2.14431i
$53$	2.21350	+	1.60820i	0.304047	+	0.220903i	0.729338	−	0.684153i	$-0.239828\pi$
$53$	2.21350	+	1.60820i	0.304047	+	0.220903i	−0.425291	+	0.905057i	$0.639828\pi$
$54$	−2.75230	−	12.6131i	−0.374541	−	1.71643i
$55$	−1.14276	+	0.112945i	−0.154090	+	0.0152295i
$56$	0.727395	+	6.92070i	0.0972023	+	0.924818i
$57$	−8.11140	+	3.97429i	−1.07438	+	0.526408i
$58$	15.7279	+	7.00251i	2.06517	+	0.919475i
$59$	−2.04720	+	2.27364i	−0.266522	+	0.296003i	−0.861519	−	0.507725i	$-0.830487\pi$
$59$	−2.04720	+	2.27364i	−0.266522	+	0.296003i	0.594997	+	0.803728i	$0.297153\pi$
$60$	9.89368	+	12.7789i	1.27727	+	1.64975i
$61$	4.90975	+	5.45283i	0.628630	+	0.698164i	0.970368	−	0.241631i	$-0.0776824\pi$
$61$	4.90975	+	5.45283i	0.628630	+	0.698164i	−0.341739	+	0.939795i	$0.611016\pi$
$62$	1.18008	+	3.63190i	0.149870	+	0.461251i
$63$	−2.95344	+	2.49642i	−0.372099	+	0.314519i
$64$	−1.75586	+	5.40400i	−0.219483	+	0.675499i
$65$	−2.25049	−	10.9204i	−0.279139	−	1.35451i
$66$	−0.605320	+	2.12544i	−0.0745098	+	0.261624i
$67$	−0.415400	−	0.184948i	−0.0507492	−	0.0225950i	0.381205	−	0.924490i	$-0.375509\pi$
$67$	−0.415400	−	0.184948i	−0.0507492	−	0.0225950i	−0.431954	+	0.901895i	$0.642176\pi$
$68$	14.4568	+	25.0399i	1.75314	+	3.03654i
$69$	−7.21258	+	0.264873i	−0.868292	+	0.0318870i
$70$	2.95334	−	6.52406i	0.352991	−	0.779775i
$71$	1.33759	+	0.971819i	0.158743	+	0.115334i	0.664321	−	0.747447i	$-0.268721\pi$
$71$	1.33759	+	0.971819i	0.158743	+	0.115334i	−0.505578	+	0.862781i	$0.668721\pi$
$72$	15.5516	−	4.52004i	1.83278	−	0.532692i
$73$	−2.72548	+	8.38816i	−0.318993	+	0.981760i	0.655086	+	0.755554i	$0.272632\pi$
$73$	−2.72548	+	8.38816i	−0.318993	+	0.981760i	−0.974079	+	0.226206i	$0.927368\pi$
$74$	9.13854	−	15.8284i	1.06233	−	1.84002i
$75$	−1.11424	−	8.58828i	−0.128661	−	0.991689i
$76$	−10.8807	−	18.8459i	−1.24810	−	2.16178i
$77$	0.647525	−	0.137636i	0.0737923	−	0.0156850i
$78$	−21.1387	−	3.68808i	−2.39348	−	0.417593i
$79$	−3.14525	+	1.40036i	−0.353869	+	0.157553i	−0.575969	−	0.817471i	$-0.695375\pi$
$79$	−3.14525	+	1.40036i	−0.353869	+	0.157553i	0.222101	+	0.975024i	$0.428709\pi$
$80$	−8.46644	+	7.52863i	−0.946577	+	0.841727i
$81$	6.93589	+	5.73528i	0.770654	+	0.637253i
$82$	−10.1232			−1.11792
$83$	−1.53461	−	14.6009i	−0.168446	−	1.60265i	−0.673247	−	0.739417i	$-0.735101\pi$
$83$	−1.53461	−	14.6009i	−0.168446	−	1.60265i	0.504802	−	0.863235i	$-0.331566\pi$
$84$	−6.48396	−	6.69019i	−0.707458	−	0.729960i
$85$	0.0961272	−	15.4935i	0.0104265	−	1.68051i
$86$	−10.1274	+	2.15265i	−1.09207	+	0.232126i
$87$	−11.6404	+	2.92455i	−1.24798	+	0.313545i
$88$	−2.71176	−	0.576402i	−0.289074	−	0.0614446i
$89$	−2.98202	+	9.17771i	−0.316093	+	0.972835i	0.659209	+	0.751960i	$0.270891\pi$
$89$	−2.98202	+	9.17771i	−0.316093	+	0.972835i	−0.975302	+	0.220875i	$0.929109\pi$
$90$	−16.1610	−	4.07410i	−1.70352	−	0.429448i
$91$	1.98628	+	6.11314i	0.208219	+	0.640831i
$92$	−1.81755	−	17.2928i	−0.189493	−	1.80290i
$93$	−2.20977	−	1.48473i	−0.229142	−	0.153959i
$94$	18.2804	+	8.13897i	1.88548	+	0.839471i
$95$	−0.0723487	+	11.6610i	−0.00742282	+	1.19639i
$96$	1.06663	+	2.91421i	0.108863	+	0.297430i
$97$	7.36689	−	3.27995i	0.747994	−	0.333028i	0.00290713	−	0.999996i	$-0.499075\pi$
$97$	7.36689	−	3.27995i	0.747994	−	0.333028i	0.745087	+	0.666967i	$0.232408\pi$
$98$	4.09855	−	12.6140i	0.414016	−	1.27421i
$99$	−0.582277	−	1.42637i	−0.0585210	−	0.143356i
$100$	20.4604	−	4.08432i	2.04604	−	0.408432i
$101$	−7.80298	+	13.5152i	−0.776425	+	1.34481i	0.157565	+	0.987509i	$0.449636\pi$
$101$	−7.80298	+	13.5152i	−0.776425	+	1.34481i	−0.933990	+	0.357299i	$0.883698\pi$
$102$	−27.6666	−	11.1201i	−2.73940	−	1.10106i
$103$	−1.58857	+	15.1142i	−0.156526	+	1.48925i	0.580986	+	0.813913i	$0.302667\pi$
$103$	−1.58857	+	15.1142i	−0.156526	+	1.48925i	−0.737512	+	0.675334i	$0.764000\pi$
$104$	2.81376	−	26.7711i	0.275912	−	2.62512i
$105$	1.18645	+	4.84946i	0.115785	+	0.473258i
$106$	−0.710555	−	6.76048i	−0.0690152	−	0.656636i
$107$	−10.6981			−1.03422			−0.517111	−	0.855919i	$-0.672992\pi$
$107$	−10.6981			−1.03422			−0.517111	+	0.855919i	$0.672992\pi$
$108$	−12.6498	+	17.6102i	−1.21722	+	1.69454i
$109$	−4.10780	−	12.6425i	−0.393456	−	1.21093i	−0.930158	−	0.367160i	$-0.880330\pi$
$109$	−4.10780	−	12.6425i	−0.393456	−	1.21093i	0.536702	−	0.843772i	$-0.319670\pi$
$110$	2.10834	+	1.92217i	0.201022	+	0.183272i
$111$	1.79601	+	12.6144i	0.170470	+	1.19731i
$112$	4.37032	−	4.85373i	0.412956	−	0.458635i
$113$	−6.37245	+	7.07732i	−0.599470	+	0.665778i	−0.964151	−	0.265354i	$-0.914511\pi$
$113$	−6.37245	+	7.07732i	−0.599470	+	0.665778i	0.364681	+	0.931132i	$0.381178\pi$
$114$	20.8229	+	8.36940i	1.95024	+	0.783866i
$115$	−3.84258	+	8.48844i	−0.358322	+	0.791551i
$116$	−8.93533	−	27.5001i	−0.829625	−	2.55332i
$117$	13.1828	−	7.07044i	1.21875	−	0.653662i
$118$	7.60135			0.699761
$119$	0.933637	+	8.88297i	0.0855864	+	0.814300i
$120$	3.72126	−	20.5741i	0.339703	−	1.87815i
$121$	1.12225	−	10.6775i	0.102022	−	0.970678i
$122$	1.90557	−	18.1303i	0.172522	−	1.64144i
$123$	5.55336	−	4.35489i	0.500730	−	0.392667i
$124$	3.20690	−	5.55451i	0.287988	−	0.498810i
$125$	−10.5670	−	3.65222i	−0.945140	−	0.326664i
$126$	9.51927	+	1.30290i	0.848044	+	0.116072i
$127$	4.08839	−	12.5828i	0.362786	−	1.11654i	−0.588570	−	0.808447i	$-0.700309\pi$
$127$	4.08839	−	12.5828i	0.362786	−	1.11654i	0.951356	−	0.308094i	$-0.0996913\pi$
$128$	16.1703	−	7.19949i	1.42927	−	0.636351i
$129$	4.62964	−	5.53761i	0.407617	−	0.487559i
$130$	−16.4217	+	22.3101i	−1.44027	+	1.95672i
$131$	9.15975	+	4.07819i	0.800291	+	0.356313i	0.765789	−	0.643092i	$-0.222349\pi$
$131$	9.15975	+	4.07819i	0.800291	+	0.356313i	0.0345024	+	0.999405i	$0.489015\pi$
$132$	3.33311	−	1.63310i	0.290110	−	0.142143i
$133$	−0.702688	−	6.68563i	−0.0609308	−	0.579718i
$134$	0.349108	+	1.07445i	0.0301584	+	0.0928179i
$135$	10.6182	−	4.71734i	0.913871	−	0.406004i
$136$	11.5590	−	35.5749i	0.991176	−	3.05053i
$137$	−10.3384	−	2.19749i	−0.883268	−	0.187744i	−0.256121	−	0.966645i	$-0.582444\pi$
$137$	−10.3384	−	2.19749i	−0.883268	−	0.187744i	−0.627148	+	0.778900i	$0.715778\pi$
$138$	12.4797	+	12.8766i	1.06234	+	1.09613i
$139$	−0.581824	+	0.123671i	−0.0493497	+	0.0104896i	−0.232520	−	0.972592i	$-0.574697\pi$
$139$	−0.581824	+	0.123671i	−0.0493497	+	0.0104896i	0.183171	+	0.983081i	$0.441364\pi$
$140$	−11.4619	+	3.64574i	−0.968710	+	0.308122i
$141$	−13.5296	+	3.39919i	−1.13939	+	0.286263i
$142$	−0.429381	−	4.08529i	−0.0360329	−	0.342830i
$143$	−2.56076			−0.214141
$144$	−12.9195	−	8.00847i	−1.07663	−	0.667372i
$145$	−3.31550	+	15.1358i	−0.275338	+	1.25696i
$146$	20.0185	−	8.91283i	1.65675	−	0.737631i
$147$	3.17805	+	8.68295i	0.262122	+	0.716158i
$148$	−30.0261	+	6.38224i	−2.46813	+	0.524617i
$149$	−1.01642	−	1.76049i	−0.0832683	−	0.144225i	0.821384	−	0.570376i	$-0.193203\pi$
$149$	−1.01642	−	1.76049i	−0.0832683	−	0.144225i	−0.904652	+	0.426151i	$0.859869\pi$
$150$	−14.0046	+	16.3350i	−1.14347	+	1.33375i
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	−0.938836	−	0.344363i	$-0.888095\pi$
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	0.767646	+	0.640874i	$0.221428\pi$
$152$	−8.69971	+	26.7750i	−0.705640	+	2.17174i
$153$	19.9611	−	5.80163i	1.61376	−	0.469034i
$154$	−1.33061	−	0.966746i	−0.107224	−	0.0779027i
$155$	−2.98707	+	1.69996i	−0.239927	+	0.136544i
$156$	19.1529	+	30.5287i	1.53346	+	2.44425i
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	0.876948	−	0.480585i	$-0.159576\pi$
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	−0.854673	+	0.519167i	$0.826242\pi$
$158$	7.81443	+	3.47921i	0.621683	+	0.276791i
$159$	3.29808	+	3.40298i	0.261555	+	0.269874i
$160$	3.98169	+	0.443485i	0.314780	+	0.0350606i
$161$	1.65988	−	5.10858i	0.130817	−	0.402612i
$162$	−0.941316	−	22.3408i	−0.0739568	−	1.75526i
$163$	−5.35439	−	16.4791i	−0.419388	−	1.29074i	−0.908267	−	0.418392i	$-0.862594\pi$
$163$	−5.35439	−	16.4791i	−0.419388	−	1.29074i	0.488879	−	0.872352i	$-0.337406\pi$
$164$	11.3767	+	12.6351i	0.888369	+	0.986634i
$165$	−1.98349	−	0.147479i	−0.154414	−	0.0114812i
$166$	−24.4071	+	27.1069i	−1.89436	+	2.10390i
$167$	−5.98923	−	2.66658i	−0.463461	−	0.206346i	0.161703	−	0.986839i	$-0.448301\pi$
$167$	−5.98923	−	2.66658i	−0.463461	−	0.206346i	−0.625164	+	0.780493i	$0.714968\pi$
$168$	−0.819125	+	12.0252i	−0.0631969	+	0.927762i
$169$	−1.24014	−	11.7992i	−0.0953956	−	0.907628i
$170$	−28.7663	+	25.5799i	−2.20627	+	1.96189i
$171$	−15.0234	+	4.36651i	−1.14887	+	0.333915i
$172$	14.0682	+	10.2212i	1.07269	+	0.779357i
$173$	−0.719368	−	0.798939i	−0.0546925	−	0.0607422i	0.715178	−	0.698943i	$-0.246346\pi$
$173$	−0.719368	−	0.798939i	−0.0546925	−	0.0607422i	−0.769870	+	0.638200i	$0.779679\pi$
$174$	24.7515	+	16.6303i	1.87641	+	1.26074i
$175$	6.28731	+	1.41817i	0.475276	+	0.107204i
$176$	1.30102	+	2.25343i	0.0980678	+	0.169858i
$177$	−4.16994	+	3.27002i	−0.313432	+	0.245790i
$178$	21.9028	−	9.75176i	1.64168	−	0.730925i
$179$	15.2398	+	11.0724i	1.13908	+	0.827587i	0.986990	−	0.160781i	$-0.0514012\pi$
$179$	15.2398	+	11.0724i	1.13908	+	0.827587i	0.152085	+	0.988367i	$0.451401\pi$
$180$	13.0771	+	24.7497i	0.974711	+	1.84473i
$181$	−11.6647	+	8.47488i	−0.867029	+	0.629933i	−0.929788	−	0.368096i	$-0.880010\pi$
$181$	−11.6647	+	8.47488i	−0.867029	+	0.629933i	0.0627594	+	0.998029i	$0.480010\pi$
$182$	7.98490	−	13.8303i	0.591880	−	1.02517i
$183$	6.75411	+	10.7656i	0.499278	+	0.795820i
$184$	−15.0521	+	16.7171i	−1.10966	+	1.23240i
$185$	15.6125	+	5.18011i	1.14785	+	0.380849i
$186$	0.932334	+	6.54832i	0.0683621	+	0.480146i
$187$	−3.48064	−	0.739832i	−0.254529	−	0.0541019i
$188$	−10.3855	−	31.9632i	−0.757439	−	2.33116i
$189$	−5.78256	+	3.38035i	−0.420620	+	0.245884i
$190$	21.6505	−	19.2523i	1.57069	−	1.39671i
$191$	18.1108	+	3.84958i	1.31046	+	0.278546i	0.809598	−	0.586984i	$-0.199685\pi$
$191$	18.1108	+	3.84958i	1.31046	+	0.278546i	0.500857	+	0.865530i	$0.333018\pi$
$192$	−4.60473	+	8.69799i	−0.332318	+	0.627724i
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	0.752311	−	0.658808i	$-0.228939\pi$
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	−0.946700	+	0.322117i	$0.895606\pi$
$194$	−18.3031	−	8.14909i	−1.31409	−	0.585070i
$195$	−0.588990	−	19.3033i	−0.0421785	−	1.38233i
$196$	−20.3501	+	9.06044i	−1.45358	+	0.647174i
$197$	−12.6037	−	9.15716i	−0.897980	−	0.652421i	0.0399665	−	0.999201i	$-0.487275\pi$
$197$	−12.6037	−	9.15716i	−0.897980	−	0.652421i	−0.937946	+	0.346780i	$0.887275\pi$
$198$	−1.66558	+	3.44639i	−0.118367	+	0.244924i
$199$	−17.1285			−1.21421			−0.607104	−	0.794623i	$-0.707669\pi$
$199$	−17.1285			−1.21421			−0.607104	+	0.794623i	$0.707669\pi$
$200$	−21.6384	−	16.1352i	−1.53007	−	1.14093i
$201$	−0.653729	−	0.439235i	−0.0461105	−	0.0309812i
$202$	37.9260	−	8.06141i	2.66846	−	0.567199i
$203$	0.933693	−	8.88350i	0.0655324	−	0.623499i
$204$	17.2130	+	47.0287i	1.20515	+	3.29267i
$205$	−1.83893	−	8.92336i	−0.128436	−	0.623235i
$206$	30.5471	−	22.1938i	2.12832	−	1.54631i
$207$	−12.3855	−	1.69520i	−0.860852	−	0.117825i
$208$	−20.4398	+	14.8504i	−1.41724	+	1.02969i
$209$	2.61965	+	0.556824i	0.181205	+	0.0385163i
$210$	6.98139	−	10.2527i	0.481762	−	0.707500i
$211$	14.1558	−	3.00892i	0.974529	−	0.207142i	0.306986	−	0.951714i	$-0.400680\pi$
$211$	14.1558	−	3.00892i	0.974529	−	0.207142i	0.667543	+	0.744572i	$0.267346\pi$
$212$	−7.63944	+	8.48446i	−0.524679	+	0.582715i
$213$	1.99300	+	2.05639i	0.136558	+	0.140901i
$214$	17.7852	+	19.7524i	1.21577	+	1.35025i
$215$	−3.73721	−	8.53606i	−0.254876	−	0.582154i
$216$	27.8810	−	3.08278i	1.89706	−	0.209757i
$217$	1.60293	−	1.16460i	0.108814	−	0.0790579i
$218$	−16.5135	+	28.6022i	−1.11843	+	1.93718i
$219$	−7.14754	+	13.5012i	−0.482986	+	0.912324i
$220$	0.0297293	−	4.79168i	0.00200435	−	0.323055i
$221$	3.61156	−	34.3617i	0.242939	−	2.31141i
$222$	20.3049	−	24.2871i	1.36278	−	1.63005i
$223$	−12.4797	−	13.8601i	−0.835699	−	0.928138i	0.162585	−	0.986695i	$-0.448017\pi$
$223$	−12.4797	−	13.8601i	−0.835699	−	0.928138i	−0.998284	+	0.0585563i	$0.981350\pi$
$224$	−2.30957			−0.154314
$225$	0.655497	−	14.9857i	0.0436998	−	0.999045i
$226$	23.6612			1.57392
$227$	11.3804	+	12.6392i	0.755341	+	0.838891i	0.991128	−	0.132914i	$-0.0424333\pi$
$227$	11.3804	+	12.6392i	0.755341	+	0.838891i	−0.235787	+	0.971805i	$0.575767\pi$
$228$	−12.9551	−	35.3955i	−0.857974	−	2.34412i
$229$	2.27581	−	21.6529i	0.150390	−	1.43086i	−0.615626	−	0.788039i	$-0.711097\pi$
$229$	2.27581	−	21.6529i	0.150390	−	1.43086i	0.766015	−	0.642823i	$-0.222237\pi$
$230$	22.0608	−	7.01698i	1.45465	−	0.462686i
$231$	1.14583	−	0.0420792i	0.0753901	−	0.00276861i
$232$	−18.7040	+	32.3962i	−1.22798	+	2.12692i
$233$	−7.60150	+	5.52281i	−0.497991	+	0.361811i	−0.808249	−	0.588841i	$-0.799584\pi$
$233$	−7.60150	+	5.52281i	−0.497991	+	0.361811i	0.310258	+	0.950652i	$0.399584\pi$
$234$	−34.9705	−	12.5858i	−2.28609	−	0.822758i
$235$	−3.85359	+	17.5923i	−0.251380	+	1.14759i
$236$	−8.54258	−	9.48750i	−0.556075	−	0.617583i
$237$	−5.78355	+	1.45307i	−0.375682	+	0.0943869i
$238$	14.8490	−	16.4915i	0.962516	−	1.06898i
$239$	−4.80649	+	1.02165i	−0.310906	+	0.0660851i	−0.360722	−	0.932673i	$-0.617470\pi$
$239$	−4.80649	+	1.02165i	−0.310906	+	0.0660851i	0.0498163	+	0.998758i	$0.484136\pi$
$240$	−16.6873	+	10.3255i	−1.07716	+	0.666508i
$241$	7.81201	+	1.66049i	0.503216	+	0.106962i	0.452524	−	0.891752i	$-0.350524\pi$
$241$	7.81201	+	1.66049i	0.503216	+	0.106962i	0.0506924	+	0.998714i	$0.483857\pi$
$242$	−21.5801	+	15.6788i	−1.38722	+	1.00787i
$243$	10.1272	+	11.8508i	0.649659	+	0.760226i
$244$	−24.7706	+	17.9969i	−1.58577	+	1.15213i
$245$	11.8635	+	1.32137i	0.757933	+	0.0844195i
$246$	−17.2729	−	3.01362i	−1.10128	−	0.192142i
$247$	−2.71818	+	25.8618i	−0.172954	+	1.64555i
$248$	−8.11624	+	1.72516i	−0.515382	+	0.109548i
$249$	1.72814	−	25.3699i	0.109516	−	1.60775i
$250$	10.8240	+	25.5821i	0.684568	+	1.61795i
$251$	21.5099			1.35769			0.678847	−	0.734279i	$-0.262480\pi$
$251$	21.5099			1.35769			0.678847	+	0.734279i	$0.262480\pi$
$252$	−9.07179	−	13.3456i	−0.571469	−	0.840691i
$253$	1.73126	+	1.25783i	0.108843	+	0.0790792i
$254$	−30.0291	+	13.3698i	−1.88419	+	0.838897i
$255$	4.77636	−	26.4076i	0.299107	−	1.65371i
$256$	−29.7937	−	13.2650i	−1.86211	−	0.829063i
$257$	4.80713	+	8.32619i	0.299860	+	0.519373i	0.976104	−	0.217305i	$-0.0697266\pi$
$257$	4.80713	+	8.32619i	0.299860	+	0.519373i	−0.676243	+	0.736678i	$0.736393\pi$
$258$	−17.9210	+	0.658127i	−1.11571	+	0.0409732i
$259$	−9.27556	−	1.97158i	−0.576356	−	0.122508i
$260$	46.3010	−	4.57618i	2.87147	−	0.283803i
$261$	−20.7324	+	1.52480i	−1.28330	+	0.0943826i
$262$	−7.69800	−	23.6920i	−0.475584	−	1.46370i
$263$	−9.44631	−	2.00788i	−0.582484	−	0.123811i	−0.0927605	−	0.995688i	$-0.529569\pi$
$263$	−9.44631	−	2.00788i	−0.582484	−	0.123811i	−0.489724	+	0.871878i	$0.662902\pi$
$264$	−4.45541	−	1.79078i	−0.274212	−	0.110215i
$265$	5.83014	−	1.85442i	0.358143	−	0.113916i
$266$	−11.1759	+	12.4120i	−0.685236	+	0.761031i
$267$	−7.82031	+	14.7720i	−0.478595	+	0.904030i
$268$	0.948715	−	1.64322i	0.0579520	−	0.100376i
$269$	14.7015	−	10.6812i	0.896364	−	0.651246i	−0.0411659	−	0.999152i	$-0.513107\pi$
$269$	14.7015	−	10.6812i	0.896364	−	0.651246i	0.937529	+	0.347906i	$0.113107\pi$
$270$	−26.3623	−	11.7626i	−1.60436	−	0.715849i
$271$	−2.02436	−	1.47078i	−0.122971	−	0.0893437i	0.524600	−	0.851349i	$-0.324215\pi$
$271$	−2.02436	−	1.47078i	−0.122971	−	0.0893437i	−0.647571	+	0.762005i	$0.724215\pi$
$272$	−32.0726	+	14.2796i	−1.94469	+	0.865831i
$273$	1.56929	+	11.0220i	0.0949775	+	0.667082i
$274$	13.1299	+	22.7416i	0.793204	+	1.37387i
$275$	−1.31136	+	2.20763i	−0.0790783	+	0.133125i
$276$	2.04676	−	30.0474i	0.123200	−	1.80864i
$277$	9.01502	+	10.0122i	0.541660	+	0.601574i	0.950382	−	0.311084i	$-0.100692\pi$
$277$	9.01502	+	10.0122i	0.541660	+	0.601574i	−0.408722	+	0.912659i	$0.634026\pi$
$278$	1.19560	+	0.868656i	0.0717075	+	0.0520985i
$279$	−3.32848	−	3.19119i	−0.199271	−	0.191052i
$280$	13.4272	+	7.86366i	0.802427	+	0.469944i
$281$	0.0790201	+	0.751826i	0.00471394	+	0.0448502i	0.996626	−	0.0820768i	$-0.0261553\pi$
$281$	0.0790201	+	0.751826i	0.00471394	+	0.0448502i	−0.991912	+	0.126927i	$0.959489\pi$
$282$	28.7685	+	19.3293i	1.71314	+	1.15105i
$283$	−3.82568	−	1.70330i	−0.227413	−	0.101251i	0.289867	−	0.957067i	$-0.406389\pi$
$283$	−3.82568	−	1.70330i	−0.227413	−	0.101251i	−0.517280	+	0.855816i	$0.673055\pi$
$284$	−4.61644	+	5.12707i	−0.273935	+	0.304236i
$285$	−3.59486	+	19.8753i	−0.212941	+	1.17731i
$286$	4.25717	+	4.72806i	0.251732	+	0.279576i
$287$	1.62304	+	4.99519i	0.0958049	+	0.294857i
$288$	0.952422	+	5.28998i	0.0561220	+	0.311715i
$289$	9.58309	−	29.4937i	0.563711	−	1.73492i
$290$	33.4581	−	19.0412i	1.96472	−	1.11814i
$291$	13.5464	−	3.40341i	0.794102	−	0.199511i
$292$	−33.6217	−	14.9694i	−1.96756	−	0.876016i
$293$	−13.1006	−	22.6909i	−0.765344	−	1.32561i	−0.940065	−	0.340997i	$-0.889236\pi$
$293$	−13.1006	−	22.6909i	−0.765344	−	1.32561i	0.174721	−	0.984618i	$-0.444098\pi$
$294$	10.7484	−	20.3029i	0.626860	−	1.18409i
$295$	1.38083	+	6.70042i	0.0803948	+	0.390114i
$296$	32.1283	+	23.3426i	1.86742	+	1.35676i
$297$	−0.568900	−	2.60713i	−0.0330109	−	0.151281i
$298$	−1.56073	+	4.80343i	−0.0904105	+	0.278255i
$299$	−10.3891	+	17.9945i	−0.600819	+	1.04065i
$300$	36.1270	−	0.878013i	2.08579	−	0.0506921i
$301$	2.68592	+	4.65215i	0.154814	+	0.268146i
$302$	10.2246	−	2.17330i	0.588358	−	0.125059i
$303$	−17.3374	+	20.7377i	−0.996010	+	1.19135i
$304$	24.1390	−	10.7474i	1.38447	−	0.616404i
$305$	16.3276	−	1.61375i	0.934917	−	0.0924029i
$306$	−43.8965	−	27.2102i	−2.50939	−	1.55551i
$307$	13.6647			0.779887			0.389944	−	0.920839i	$-0.372495\pi$
$307$	13.6647			0.779887			0.389944	+	0.920839i	$0.372495\pi$
$308$	0.288746	+	2.74724i	0.0164528	+	0.156538i
$309$	−7.20996	+	25.3161i	−0.410160	+	1.44018i
$310$	8.10464	+	2.68906i	0.460313	+	0.152729i
$311$	−0.934468	+	0.198627i	−0.0529888	+	0.0112631i	−0.234330	−	0.972157i	$-0.575290\pi$
$311$	−0.934468	+	0.198627i	−0.0529888	+	0.0112631i	0.181341	+	0.983420i	$0.441956\pi$
$312$	12.7707	−	44.8412i	0.722997	−	2.53864i
$313$	11.7240	+	2.49201i	0.662680	+	0.140857i	0.526960	−	0.849890i	$-0.323332\pi$
$313$	11.7240	+	2.49201i	0.662680	+	0.140857i	0.135720	+	0.990747i	$0.456665\pi$
$314$	0.428576	−	1.31902i	0.0241859	−	0.0744367i
$315$	0.580746	+	8.62771i	0.0327213	+	0.486116i
$316$	−4.43953	−	13.6635i	−0.249743	−	0.768631i
$317$	−0.235992	−	2.24531i	−0.0132546	−	0.126109i	0.985894	−	0.167373i	$-0.0535284\pi$
$317$	−0.235992	−	2.24531i	−0.0132546	−	0.126109i	−0.999148	+	0.0412635i	$0.986862\pi$
$318$	0.800161	−	11.7468i	0.0448708	−	0.658726i
$319$	3.25095	+	1.44742i	0.182018	+	0.0810398i
$320$	7.40422	+	10.3251i	0.413908	+	0.577193i
$321$	−18.2539	−	3.18477i	−1.01883	−	0.177756i
$322$	−12.1917	+	5.42811i	−0.679419	+	0.302497i
$323$	−11.1664	+	34.3666i	−0.621314	+	1.91221i
$324$	−26.8265	+	26.2821i	−1.49036	+	1.46011i
$325$	−22.6489	−	10.4226i	−1.25634	−	0.578141i
$326$	−21.5248	+	37.2821i	−1.19215	+	2.06486i
$327$	−3.24542	−	22.7945i	−0.179472	−	1.26054i
$328$	2.29919	−	21.8753i	0.126952	−	1.20786i
$329$	1.08523	−	10.3252i	0.0598304	−	0.569248i
$330$	3.02518	+	3.90740i	0.166531	+	0.215095i
$331$	−1.40101	−	13.3298i	−0.0770067	−	0.732669i	−0.963097	−	0.269156i	$-0.913255\pi$
$331$	−1.40101	−	13.3298i	−0.0770067	−	0.732669i	0.886090	−	0.463513i	$-0.153411\pi$
$332$	61.2623			3.36221
$333$	−0.690766	+	22.0584i	−0.0378538	+	1.20879i
$334$	5.03344	+	15.4913i	0.275418	+	0.847649i
$335$	−0.883683	+	0.502910i	−0.0482807	+	0.0274769i
$336$	8.90190	−	6.98078i	0.485639	−	0.380833i
$337$	8.05962	−	8.95111i	0.439035	−	0.487598i	−0.482498	−	0.875897i	$-0.660270\pi$
$337$	8.05962	−	8.95111i	0.439035	−	0.487598i	0.921534	+	0.388299i	$0.126937\pi$
$338$	−19.7238	+	21.9054i	−1.07283	+	1.19150i
$339$	−12.9800	+	10.1788i	−0.704979	+	0.552837i
$340$	64.2554	+	7.15685i	3.48474	+	0.388135i
$341$	0.243921	+	0.750712i	0.0132091	+	0.0406533i
$342$	33.0380	+	20.4794i	1.78649	+	1.10740i
$343$	−15.9048			−0.858777
$344$	−2.35154	−	22.3734i	−0.126786	−	1.20629i
$345$	−9.08347	+	13.3397i	−0.489038	+	0.718186i
$346$	−0.279201	+	2.65642i	−0.0150099	+	0.142810i
$347$	−0.0730635	+	0.695153i	−0.00392226	+	0.0373178i	−0.996308	−	0.0858512i	$-0.972639\pi$
$347$	−0.0730635	+	0.695153i	−0.00392226	+	0.0373178i	0.992386	+	0.123169i	$0.0393057\pi$
$348$	−7.05948	−	49.5828i	−0.378428	−	2.65792i
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	−0.535773	−	0.844362i	$-0.679980\pi$
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	0.999126	+	0.0418117i	$0.0133130\pi$
$350$	−7.83399	−	13.9663i	−0.418744	−	0.746528i
$351$	24.5983	−	8.13966i	1.31296	−	0.434463i
$352$	0.284330	−	0.875079i	0.0151549	−	0.0466419i
$353$	−4.82374	+	2.14767i	−0.256742	+	0.114309i	−0.531072	−	0.847327i	$-0.678211\pi$
$353$	−4.82374	+	2.14767i	−0.256742	+	0.114309i	0.274330	+	0.961636i	$0.411544\pi$
$354$	12.9700	+	2.26289i	0.689347	+	0.120271i
$355$	3.52310	−	1.12061i	0.186986	−	0.0594756i
$356$	−36.7864	−	16.3784i	−1.94968	−	0.868052i
$357$	−1.05138	+	15.4347i	−0.0556447	+	0.816893i
$358$	−4.89212	−	46.5455i	−0.258557	−	2.46000i
$359$	0.334961	+	1.03090i	0.0176786	+	0.0544091i	0.959507	−	0.281686i	$-0.0908937\pi$
$359$	0.334961	+	1.03090i	0.0176786	+	0.0544091i	−0.941828	+	0.336095i	$0.890894\pi$
$360$	12.4743	−	33.9973i	0.657453	−	1.79181i
$361$	2.53289	−	7.79543i	0.133310	−	0.410286i
$362$	35.0398	+	7.44793i	1.84165	+	0.391455i
$363$	5.09349	−	17.8846i	0.267339	−	0.938698i
$364$	−26.2356	+	5.57656i	−1.37512	+	0.292291i
$365$	11.4929	+	16.0268i	0.601568	+	0.838884i
$366$	8.64874	−	30.3680i	0.452077	−	1.58736i
$367$	−3.26474	−	31.0619i	−0.170418	−	1.62142i	−0.661251	−	0.750165i	$-0.729974\pi$
$367$	−3.26474	−	31.0619i	−0.170418	−	1.62142i	0.490833	−	0.871254i	$-0.336692\pi$
$368$	21.1132			1.10060
$369$	10.7720	−	5.77743i	0.560768	−	0.300761i
$370$	−16.3909	−	37.4379i	−0.852121	−	1.94630i
$371$	−3.22198	+	1.43452i	−0.167277	+	0.0744764i
$372$	7.12540	−	8.52284i	0.369435	−	0.441889i
$373$	0.241813	−	0.0513989i	0.0125206	−	0.00266133i	−0.201647	−	0.979458i	$-0.564629\pi$
$373$	0.241813	−	0.0513989i	0.0125206	−	0.00266133i	0.214168	+	0.976797i	$0.431296\pi$
$374$	4.42044	+	7.65643i	0.228576	+	0.395905i
$375$	−16.9430	−	9.37744i	−0.874930	−	0.484249i
$376$	−21.7395	+	37.6539i	−1.12113	+	1.94185i
$377$	−10.6775	+	32.8619i	−0.549917	+	1.69247i
$378$	15.8546	+	5.05696i	0.815474	+	0.260102i
$379$	18.0726	+	13.1305i	0.928325	+	0.674467i	0.945582	−	0.325384i	$-0.105493\pi$
$379$	18.0726	+	13.1305i	0.928325	+	0.674467i	−0.0172574	+	0.999851i	$0.505493\pi$
$380$	−48.3609	−	5.38650i	−2.48086	−	0.276321i
$381$	10.7218	−	20.2526i	0.549292	−	1.03757i
$382$	−23.0010	−	39.8388i	−1.17683	−	2.03833i
$383$	24.2261	+	10.7861i	1.23789	+	0.551146i	0.918103	−	0.396342i	$-0.129720\pi$
$383$	24.2261	+	10.7861i	1.23789	+	0.551146i	0.319792	+	0.947488i	$0.396387\pi$
$384$	29.7343	−	7.47048i	1.51737	−	0.381227i
$385$	0.610453	−	1.34852i	0.0311116	−	0.0687270i
$386$	−4.14671	+	12.7622i	−0.211062	+	0.649581i
$387$	9.54796	−	8.07046i	0.485350	−	0.410245i
$388$	10.3984	+	32.0029i	0.527898	+	1.62470i
$389$	−8.70282	−	9.66546i	−0.441250	−	0.490058i	0.480962	−	0.876741i	$-0.340287\pi$
$389$	−8.70282	−	9.66546i	−0.441250	−	0.490058i	−0.922213	+	0.386683i	$0.873621\pi$
$390$	−34.6615	+	33.1785i	−1.75515	+	1.68006i
$391$	−19.3200	+	21.4570i	−0.977052	+	1.08513i
$392$	26.3270	+	11.7215i	1.32971	+	0.592027i
$393$	14.4150	+	9.68533i	0.727141	+	0.488560i
$394$	4.04593	+	38.4945i	0.203831	+	1.93932i
$395$	−1.64731	+	7.52027i	−0.0828854	+	0.378386i
$396$	6.17337	−	1.79427i	0.310223	−	0.0901655i
$397$	24.8748	+	18.0726i	1.24843	+	0.907040i	0.998130	−	0.0611280i	$-0.0194698\pi$
$397$	24.8748	+	18.0726i	1.24843	+	0.907040i	0.250303	+	0.968168i	$0.419470\pi$
$398$	28.4755	+	31.6253i	1.42735	+	1.58523i
$399$	0.791302	−	11.6167i	0.0396147	−	0.581564i
$400$	2.33528	+	25.2260i	0.116764	+	1.26130i
$401$	5.05931	+	8.76298i	0.252650	+	0.437602i	0.964255	−	0.264978i	$-0.0853646\pi$
$401$	5.05931	+	8.76298i	0.252650	+	0.437602i	−0.711605	+	0.702580i	$0.752031\pi$
$402$	0.275818	+	1.93723i	0.0137565	+	0.0966201i
$403$	−7.00169	+	3.11735i	−0.348779	+	0.155286i
$404$	−52.6838	−	38.2771i	−2.62112	−	1.90435i
$405$	19.5220	−	4.88808i	0.970054	−	0.242891i
$406$	−17.9543	+	13.0446i	−0.891058	+	0.647392i
$407$	1.88893	−	3.27173i	0.0936309	−	0.162173i
$408$	30.3133	−	57.2596i	1.50073	−	2.83477i
$409$	−11.8509	+	13.1617i	−0.585987	+	0.650804i	−0.961108	−	0.276171i	$-0.910934\pi$
$409$	−11.8509	+	13.1617i	−0.585987	+	0.650804i	0.375121	+	0.926976i	$0.377601\pi$
$410$	−13.4185	+	18.2301i	−0.662694	+	0.900321i
$411$	−16.9860	−	6.82722i	−0.837856	−	0.336762i
$412$	−62.0304	−	13.1850i	−3.05602	−	0.649577i
$413$	−1.21871	−	3.75082i	−0.0599690	−	0.184566i
$414$	17.4605	+	25.6862i	0.858138	+	1.26241i
$415$	−28.3278	−	16.5902i	−1.39056	−	0.814383i
$416$	8.73878	+	1.85749i	0.428454	+	0.0910707i
$417$	−1.02957	+	0.0378097i	−0.0504182	+	0.00185155i
$418$	−3.32698	−	5.76250i	−0.162728	−	0.281853i
$419$	−12.2652	−	5.46080i	−0.599193	−	0.266778i	0.0846460	−	0.996411i	$-0.473024\pi$
$419$	−12.2652	−	5.46080i	−0.599193	−	0.266778i	−0.683839	+	0.729633i	$0.739691\pi$
$420$	−20.6425	+	2.80848i	−1.00725	+	0.137040i
$421$	−29.7828	+	13.2601i	−1.45152	+	0.646260i	−0.972788	−	0.231699i	$-0.925572\pi$
$421$	−29.7828	+	13.2601i	−1.45152	+	0.646260i	−0.478736	+	0.877959i	$0.658905\pi$
$422$	−29.0891	−	21.1345i	−1.41604	−	1.02881i
$423$	−24.0971	+	1.77226i	−1.17164	+	0.0861704i
$424$	14.7702			0.717304
$425$	−27.7737	−	20.7101i	−1.34722	−	1.00459i
$426$	0.483529	−	7.09846i	0.0234271	−	0.343921i
$427$	−9.25175	+	1.96652i	−0.447724	+	0.0951666i
$428$	4.66626	−	44.3965i	0.225552	−	2.14599i
$429$	−4.36936	−	0.762325i	−0.210955	−	0.0368054i
$430$	−9.54760	+	21.0911i	−0.460426	+	1.01710i
$431$	7.24479	−	5.26365i	0.348969	−	0.253541i	−0.399467	−	0.916747i	$-0.630805\pi$
$431$	7.24479	−	5.26365i	0.348969	−	0.253541i	0.748436	+	0.663206i	$0.230805\pi$
$432$	−19.6602	−	17.5107i	−0.945902	−	0.842486i
$433$	22.5500	−	16.3836i	1.08369	−	0.787344i	0.105364	−	0.994434i	$-0.466399\pi$
$433$	22.5500	−	16.3836i	1.08369	−	0.787344i	0.978322	+	0.207090i	$0.0663992\pi$
$434$	−4.81507	−	1.02347i	−0.231131	−	0.0491284i
$435$	−10.1630	+	24.8389i	−0.487280	+	1.19094i
$436$	54.2576	−	11.5328i	2.59847	−	0.552321i
$437$	14.5409	−	16.1493i	0.695585	−	0.772525i
$438$	36.8105	−	9.24832i	1.75887	−	0.441902i
$439$	−2.10414	−	2.33689i	−0.100425	−	0.111533i	0.690837	−	0.723011i	$-0.257242\pi$
$439$	−2.10414	−	2.33689i	−0.100425	−	0.111533i	−0.791262	+	0.611477i	$0.790576\pi$
$440$	−4.63250	+	4.11937i	−0.220846	+	0.196383i
$441$	2.83776	+	15.7616i	0.135132	+	0.750553i
$442$	−69.4479	+	50.4568i	−3.30330	+	2.39999i
$443$	9.86697	−	17.0901i	0.468794	−	0.811975i	−0.530570	−	0.847641i	$-0.678022\pi$
$443$	9.86697	−	17.0901i	0.468794	−	0.811975i	0.999364	+	0.0356665i	$0.0113554\pi$
$444$	−53.1328	+	1.95124i	−2.52157	+	0.0926016i
$445$	12.5747	+	17.5354i	0.596099	+	0.831257i
$446$	−4.84360	+	46.0837i	−0.229351	+	2.18213i
$447$	−1.21020	−	3.30647i	−0.0572406	−	0.156390i
$448$	−4.90106	−	5.44318i	−0.231554	−	0.257166i
$449$	−13.7726			−0.649970			−0.324985	−	0.945719i	$-0.605359\pi$
$449$	−13.7726			−0.649970			−0.324985	+	0.945719i	$0.605359\pi$
$450$	−28.7586	+	23.7029i	−1.35569	+	1.11736i
$451$	−2.09246			−0.0985300
$452$	−26.5911	−	29.5324i	−1.25074	−	1.38909i
$453$	−4.67405	+	5.59073i	−0.219606	+	0.262675i
$454$	4.41694	−	42.0244i	0.207297	−	1.97230i
$455$	13.6416	+	4.52618i	0.639527	+	0.212190i
$456$	−22.8149	+	43.0956i	−1.06840	+	2.01814i
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	−0.614646	−	0.788803i	$-0.710701\pi$
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	0.990447	+	0.137897i	$0.0440344\pi$
$458$	−43.7623	+	31.7952i	−2.04488	+	1.48569i
$459$	35.7862	−	3.95686i	1.67036	−	0.184690i
$460$	−33.5506	−	19.6490i	−1.56431	−	0.916140i
$461$	6.87074	+	7.63073i	0.320002	+	0.355399i	0.881588	−	0.472020i	$-0.156475\pi$
$461$	6.87074	+	7.63073i	0.320002	+	0.355399i	−0.561585	+	0.827419i	$0.689808\pi$
$462$	−1.98260	−	2.04565i	−0.0922387	−	0.0951724i
$463$	12.0593	−	13.3932i	0.560444	−	0.622436i	−0.394617	−	0.918846i	$-0.629123\pi$
$463$	12.0593	−	13.3932i	0.560444	−	0.622436i	0.955061	+	0.296409i	$0.0957893\pi$
$464$	34.3427	−	7.29977i	1.59432	−	0.338883i
$465$	−5.60284	+	2.01137i	−0.259826	+	0.0932751i
$466$	22.8343	+	4.85358i	1.05778	+	0.224838i
$467$	28.5731	−	20.7596i	1.32221	−	0.960639i	0.322304	−	0.946636i	$-0.395543\pi$
$467$	28.5731	−	20.7596i	1.32221	−	0.960639i	0.999902	−	0.0140027i	$-0.00445734\pi$
$468$	23.5920	+	57.7921i	1.09054	+	2.67144i
$469$	0.474203	−	0.344529i	0.0218967	−	0.0159089i
$470$	38.8881	−	22.1315i	1.79377	−	1.02085i
$471$	0.332322	+	0.907956i	0.0153126	+	0.0418364i
$472$	−1.72643	+	16.4259i	−0.0794653	+	0.756062i
$473$	−2.09333	+	0.444951i	−0.0962515	+	0.0204589i
$474$	12.2978	+	8.26281i	0.564858	+	0.379524i
$475$	20.9035	+	15.5872i	0.959117	+	0.715189i
$476$	−37.2712			−1.70832
$477$	4.61439	+	6.78825i	0.211278	+	0.310813i
$478$	9.87695	+	7.17603i	0.451761	+	0.328224i
$479$	−1.56127	+	0.695122i	−0.0713362	+	0.0317609i	−0.442095	−	0.896968i	$-0.645764\pi$
$479$	−1.56127	+	0.695122i	−0.0713362	+	0.0317609i	0.370758	+	0.928729i	$0.379098\pi$
$480$	6.66184	+	1.94204i	0.304070	+	0.0886416i
$481$	33.5106	+	14.9199i	1.52795	+	0.680288i
$482$	−9.92134	−	17.1843i	−0.451905	−	0.782722i
$483$	4.35301	−	8.22250i	0.198069	−	0.374137i
$484$	43.8215	+	9.31455i	1.99189	+	0.423388i
$485$	3.85838	−	17.6142i	0.175200	−	0.799818i
$486$	5.04461	−	38.3998i	0.228828	−	1.74185i
$487$	10.1084	+	31.1106i	0.458057	+	1.40975i	0.867509	+	0.497422i	$0.165720\pi$
$487$	10.1084	+	31.1106i	0.458057	+	1.40975i	−0.409452	+	0.912332i	$0.634280\pi$
$488$	38.7452	+	8.23555i	1.75391	+	0.372806i
$489$	−4.23031	−	29.7119i	−0.191301	−	1.34362i
$490$	−17.2830	−	24.1010i	−0.780766	−	1.08877i
$491$	27.6113	−	30.6655i	1.24608	−	1.38391i	0.352004	−	0.935999i	$-0.385500\pi$
$491$	27.6113	−	30.6655i	1.24608	−	1.38391i	0.894077	−	0.447914i	$-0.147833\pi$
$492$	15.6503	+	24.9457i	0.705572	+	1.12464i
$493$	−24.0072	+	41.5817i	−1.08123	+	1.87275i
$494$	52.2689	−	37.9756i	2.35169	−	1.70860i
$495$	−3.34048	−	0.842115i	−0.150143	−	0.0378503i
$496$	6.30049	+	4.57758i	0.282901	+	0.205539i
$497$	−1.94701	+	0.866864i	−0.0873353	+	0.0388842i
$498$	−49.7149	+	38.9859i	−2.22778	+	1.74700i
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	0.902327	−	0.431052i	$-0.141857\pi$
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	−0.824466	+	0.565912i	$0.808524\pi$
$500$	19.7656	−	42.2596i	0.883947	−	1.88990i
$501$	−9.42546	−	6.33289i	−0.421098	−	0.282933i
$502$	−35.7595	−	39.7150i	−1.59603	−	1.77257i
$503$	13.8073	+	10.0316i	0.615638	+	0.447287i	0.851395	−	0.524525i	$-0.175757\pi$
$503$	13.8073	+	10.0316i	0.615638	+	0.447287i	−0.235757	+	0.971812i	$0.575757\pi$
$504$	−4.97749	+	20.2744i	−0.221715	+	0.903094i
$505$	13.9954	+	31.9665i	0.622788	+	1.42249i
$506$	−0.555751	−	5.28762i	−0.0247061	−	0.235063i
$507$	1.39653	−	20.5018i	0.0620222	−	0.910518i
$508$	50.4347	+	22.4550i	2.23768	+	0.996279i
$509$	5.21858	−	5.79582i	0.231309	−	0.256895i	−0.616305	−	0.787507i	$-0.711371\pi$
$509$	5.21858	−	5.79582i	0.231309	−	0.256895i	0.847615	+	0.530612i	$0.178038\pi$
$510$	−56.6983	+	35.0828i	−2.51064	+	1.55349i
$511$	−7.60751	−	8.44899i	−0.336536	−	0.373761i
$512$	14.0995	+	43.3938i	0.623115	+	1.91775i
$513$	−26.9340	+	2.97807i	−1.18916	+	0.131485i
$514$	7.38142	−	22.7177i	0.325580	−	1.00203i
$515$	25.1124	+	22.8950i	1.10658	+	1.00887i
$516$	20.9615	+	21.6282i	0.922778	+	0.952128i
$517$	3.77856	+	1.68232i	0.166181	+	0.0739884i
$518$	11.7801	+	20.4037i	0.517586	+	0.896486i
$519$	−0.989600	−	1.57736i	−0.0434386	−	0.0692386i
$520$	−44.4804	−	40.5529i	−1.95060	−	1.77836i
$521$	−9.24944	−	6.72011i	−0.405225	−	0.294413i	0.366441	−	0.930441i	$-0.380576\pi$
$521$	−9.24944	−	6.72011i	−0.405225	−	0.294413i	−0.771666	+	0.636028i	$0.780576\pi$
$522$	37.2821	+	35.7444i	1.63180	+	1.56449i
$523$	6.03668	−	18.5790i	0.263966	−	0.812403i	−0.727964	−	0.685615i	$-0.759533\pi$
$523$	6.03668	−	18.5790i	0.263966	−	0.812403i	0.991930	−	0.126788i	$-0.0404667\pi$
$524$	−20.9196	+	36.2338i	−0.913876	+	1.58288i
$525$	10.3057	+	4.29149i	0.449778	+	0.187296i
$526$	11.9969	+	20.7793i	0.523090	+	0.906019i
$527$	−10.4175	+	2.21430i	−0.453793	+	0.0964566i
$528$	1.54906	+	4.23227i	0.0674141	+	0.184186i
$529$	−5.14891	+	2.29244i	−0.223866	+	0.0996714i
$530$	−13.1163	−	7.68160i	−0.569736	−	0.333668i
$531$	−8.08853	+	4.33819i	−0.351012	+	0.188261i
$532$	28.0516			1.21619
$533$	−2.12372	−	20.2058i	−0.0919884	−	0.875211i
$534$	40.2753	−	10.1188i	1.74288	−	0.437884i
$535$	−14.1806	+	19.2654i	−0.613079	+	0.832915i
$536$	−2.40107	+	0.510364i	−0.103711	+	0.0220444i
$537$	22.7071	+	23.4293i	0.979883	+	1.01105i
$538$	−44.1620	−	9.38692i	−1.90396	−	0.404699i
$539$	0.847169	−	2.60732i	0.0364902	−	0.112305i
$540$	14.9453	+	46.1228i	0.643144	+	1.98481i
$541$	2.36879	+	7.29039i	0.101842	+	0.313439i	0.988976	−	0.148073i	$-0.0473072\pi$
$541$	2.36879	+	7.29039i	0.101842	+	0.313439i	−0.887134	+	0.461512i	$0.847307\pi$
$542$	0.649839	+	6.18281i	0.0279130	+	0.265574i
$543$	−22.4261	+	10.9880i	−0.962396	+	0.471539i
$544$	11.3413	+	5.04947i	0.486254	+	0.216494i
$545$	−28.2120	−	9.36053i	−1.20847	−	0.400961i
$546$	17.7416	−	21.2212i	0.759272	−	0.908182i
$547$	−13.1622	+	5.86017i	−0.562773	+	0.250563i	−0.668348	−	0.743849i	$-0.732998\pi$
$547$	−13.1622	+	5.86017i	−0.562773	+	0.250563i	0.105575	+	0.994411i	$0.466332\pi$
$548$	13.6289	−	41.9454i	0.582197	−	1.79182i
$549$	8.31949	+	20.3798i	0.355067	+	0.869790i
$550$	6.25616	−	1.24886i	0.266764	−	0.0532516i
$551$	18.0687	−	31.2959i	0.769751	−	1.33325i
$552$	−30.6597	+	24.0430i	−1.30496	+	1.02334i
$553$	0.463907	−	4.41378i	0.0197273	−	0.187693i
$554$	3.49890	−	33.2899i	0.148654	−	1.41435i
$555$	25.0971	+	13.4865i	1.06531	+	0.572468i
$556$	−0.259449	−	2.46849i	−0.0110031	−	0.104687i
$557$	11.9602			0.506771			0.253386	−	0.967365i	$-0.418456\pi$
$557$	11.9602			0.506771			0.253386	+	0.967365i	$0.418456\pi$
$558$	−0.358586	+	11.4508i	−0.0151802	+	0.484751i
$559$	−6.42128	−	19.7627i	−0.271591	−	0.835872i
$560$	−2.94776	−	14.3039i	−0.124566	−	0.604452i
$561$	−5.71868	−	2.29853i	−0.241443	−	0.0970439i
$562$	1.25677	−	1.39578i	0.0530136	−	0.0588776i
$563$	−27.6349	+	30.6917i	−1.16467	+	1.29350i	−0.216306	+	0.976326i	$0.569401\pi$
$563$	−27.6349	+	30.6917i	−1.16467	+	1.29350i	−0.948367	+	0.317175i	$0.897266\pi$
$564$	−8.20519	−	57.6298i	−0.345501	−	2.42665i
$565$	4.29819	+	20.8569i	0.180826	+	0.877455i
$566$	3.21516	+	9.89523i	0.135143	+	0.415928i
$567$	−10.8730	+	4.04636i	−0.456621	+	0.169931i
$568$	8.92549			0.374505
$569$	1.53101	+	14.5666i	0.0641832	+	0.610662i	0.978583	+	0.205851i	$0.0659961\pi$
$569$	1.53101	+	14.5666i	0.0641832	+	0.610662i	−0.914400	+	0.404811i	$0.867337\pi$
$570$	42.6731	−	26.4046i	1.78738	−	1.10596i
$571$	2.44705	−	23.2822i	0.102406	−	0.974328i	−0.815829	−	0.578293i	$-0.803719\pi$
$571$	2.44705	−	23.2822i	0.102406	−	0.974328i	0.918235	−	0.396035i	$-0.129614\pi$
$572$	1.11695	−	10.6270i	0.0467019	−	0.444339i
$573$	29.7561	+	11.9600i	1.24308	+	0.499635i
$574$	6.52466	−	11.3010i	0.272334	−	0.471696i
$575$	10.1928	+	18.1715i	0.425069	+	0.757803i
$576$	−10.4463	+	13.4704i	−0.435262	+	0.561265i
$577$	0.219132	−	0.674419i	0.00912259	−	0.0280764i	−0.946392	−	0.323022i	$-0.895301\pi$
$577$	0.219132	−	0.674419i	0.00912259	−	0.0280764i	0.955514	+	0.294945i	$0.0953014\pi$
$578$	−70.3874	+	31.3385i	−2.92773	+	1.30351i
$579$	−3.21539	−	8.78497i	−0.133627	−	0.365091i
$580$	−61.3670	−	20.3611i	−2.54813	−	0.845450i
$581$	17.2888	+	7.69747i	0.717261	+	0.319345i
$582$	−28.8043	−	19.3534i	−1.19398	−	0.802222i
$583$	−0.146871	−	1.39739i	−0.00608279	−	0.0578739i
$584$	14.7132	+	45.2827i	0.608838	+	1.87381i
$585$	4.74151	−	33.1120i	0.196037	−	1.36901i
$586$	−20.1161	+	61.9111i	−0.830990	+	2.55752i
$587$	10.4158	+	2.21394i	0.429905	+	0.0913791i	0.417782	−	0.908547i	$-0.362808\pi$
$587$	10.4158	+	2.21394i	0.429905	+	0.0913791i	0.0121230	+	0.999927i	$0.496141\pi$
$588$	−37.4201	+	9.40148i	−1.54318	+	0.387710i
$589$	7.84056	−	1.66656i	0.323065	−	0.0686695i
$590$	10.0758	−	13.6887i	0.414813	−	0.563555i
$591$	−18.7794	−	19.3767i	−0.772482	−	0.797052i
$592$	−3.89611	−	37.0690i	−0.160129	−	1.52353i
$593$	−47.7160			−1.95946			−0.979730	−	0.200323i	$-0.935801\pi$
$593$	−47.7160			−1.95946			−0.979730	+	0.200323i	$0.935801\pi$
$594$	−3.86791	+	5.38465i	−0.158702	+	0.220935i
$595$	17.2343	+	10.0933i	0.706535	+	0.413784i
$596$	7.74930	−	3.45021i	0.317424	−	0.141326i
$597$	−29.2260	−	5.09908i	−1.19614	−	0.208691i
$598$	50.4958	−	10.7332i	2.06493	−	0.438914i
$599$	1.95259	+	3.38199i	0.0797808	+	0.138184i	0.903155	−	0.429314i	$-0.141245\pi$
$599$	1.95259	+	3.38199i	0.0797808	+	0.138184i	−0.823374	+	0.567498i	$0.807911\pi$
$600$	−32.1178	−	33.9728i	−1.31120	−	1.38693i
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	−0.929174	−	0.369644i	$-0.879480\pi$
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	0.784708	+	0.619866i	$0.212813\pi$
$602$	4.12427	−	12.6932i	0.168093	−	0.517336i
$603$	−0.984683	−	0.944068i	−0.0400994	−	0.0384454i
$604$	−14.2032	−	10.3192i	−0.577920	−	0.419883i
$605$	−17.7407	−	16.1742i	−0.721262	−	0.657575i
$606$	67.1120	−	2.46461i	2.72624	−	0.100118i
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	0.910441	−	0.413638i	$-0.135742\pi$
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	−0.813442	+	0.581646i	$0.802409\pi$
$608$	−8.53586	−	3.80041i	−0.346175	−	0.154127i
$609$	4.23772	−	14.8797i	0.171721	−	0.602958i
$610$	−30.1237	−	27.4638i	−1.21967	−	1.11198i
$611$	−12.4103	+	38.1951i	−0.502069	+	1.54521i
$612$	15.3699	+	85.3682i	0.621293	+	3.45081i
$613$	14.0778	+	43.3269i	0.568596	+	1.74996i	0.657018	+	0.753875i	$0.271818\pi$
$613$	14.0778	+	43.3269i	0.568596	+	1.74996i	−0.0884219	+	0.996083i	$0.528182\pi$
$614$	−22.7171	−	25.2299i	−0.916789	−	1.01820i
$615$	−0.481278	−	15.7732i	−0.0194070	−	0.636035i
$616$	2.39127	−	2.65577i	0.0963469	−	0.107004i
$617$	−17.7401	−	7.89839i	−0.714189	−	0.317977i	0.0172815	−	0.999851i	$-0.494499\pi$
$617$	−17.7401	−	7.89839i	−0.714189	−	0.317977i	−0.731470	+	0.681873i	$0.761166\pi$
$618$	58.7288	−	28.7750i	2.36242	−	1.15750i
$619$	−2.85213	−	27.1362i	−0.114637	−	1.09070i	−0.888985	−	0.457936i	$-0.848589\pi$
$619$	−2.85213	−	27.1362i	−0.114637	−	1.09070i	0.774348	−	0.632760i	$-0.218078\pi$
$620$	−5.75189	−	13.1377i	−0.231001	−	0.527623i
$621$	−20.6284	−	6.57959i	−0.827790	−	0.264030i
$622$	1.92026	+	1.39515i	0.0769953	+	0.0559404i
$623$	−8.32357	−	9.24426i	−0.333477	−	0.370363i
$624$	−39.2968	+	19.2540i	−1.57313	+	0.770776i
$625$	−20.5838	+	14.1882i	−0.823354	+	0.567529i
$626$	−14.8896	−	25.7896i	−0.595109	−	1.03076i
$627$	4.30408	+	1.72995i	0.171888	+	0.0690876i
$628$	−2.12796	+	0.947428i	−0.0849148	+	0.0378065i
$629$	41.2378	+	29.9610i	1.64426	+	1.19462i
$630$	14.9643	−	15.4155i	0.596194	−	0.614169i
$631$	12.6772	−	9.21053i	0.504672	−	0.366665i	−0.306127	−	0.951991i	$-0.599033\pi$
$631$	12.6772	−	9.21053i	0.504672	−	0.366665i	0.810799	+	0.585325i	$0.199033\pi$
$632$	−9.29310	+	16.0961i	−0.369660	+	0.640269i
$633$	25.0495	−	0.919914i	0.995629	−	0.0365633i
$634$	−3.75332	+	4.16848i	−0.149063	+	0.165551i
$635$	−17.2401	−	24.0413i	−0.684154	−	0.954050i
$636$	−15.5608	+	12.2026i	−0.617025	+	0.483865i
$637$	26.0374	+	5.53442i	1.03164	+	0.219282i
$638$	−2.73215	−	8.40869i	−0.108167	−	0.332903i
$639$	2.78843	+	4.10207i	0.110309	+	0.162275i
$640$	8.46913	−	38.6631i	0.334772	−	1.52829i
$641$	−34.5500	−	7.34383i	−1.36464	−	0.290064i	−0.533348	−	0.845896i	$-0.679067\pi$
$641$	−34.5500	−	7.34383i	−1.36464	−	0.290064i	−0.831295	+	0.555832i	$0.812400\pi$
$642$	24.4662	+	38.9977i	0.965604	+	1.53911i
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	0.953304	−	0.302012i	$-0.0976583\pi$
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	−0.738202	+	0.674580i	$0.764325\pi$
$644$	20.4764	+	9.11667i	0.806882	+	0.359247i
$645$	−3.83557	−	15.6774i	−0.151025	−	0.617298i
$646$	82.0167	−	36.5162i	3.22690	−	1.43671i
$647$	−28.4306	−	20.6560i	−1.11772	−	0.812072i	−0.133860	−	0.991000i	$-0.542737\pi$
$647$	−28.4306	−	20.6560i	−1.11772	−	0.812072i	−0.983862	+	0.178928i	$0.942737\pi$
$648$	48.4904	+	3.03997i	1.90488	+	0.119421i
$649$	1.57119			0.0616748
$650$	18.4093	+	59.1451i	0.722070	+	2.31986i
$651$	3.08173	−	1.50994i	0.120783	−	0.0591791i
$652$	70.7231	−	15.0327i	2.76973	−	0.588724i
$653$	1.31892	−	12.5487i	0.0516135	−	0.491070i	−0.937929	−	0.346828i	$-0.887259\pi$
$653$	1.31892	−	12.5487i	0.0516135	−	0.491070i	0.989542	−	0.144242i	$-0.0460744\pi$
$654$	−36.6913	+	43.8872i	−1.43474	+	1.71613i
$655$	19.4856	−	11.0894i	0.761365	−	0.433299i
$656$	−16.7018	+	12.1346i	−0.652097	+	0.473776i
$657$	−16.2149	+	20.9089i	−0.632604	+	0.815734i
$658$	−20.8682	+	15.1616i	−0.813527	+	0.591062i
$659$	17.4588	+	3.71099i	0.680099	+	0.144559i	0.534993	−	0.844857i	$-0.320314\pi$
$659$	17.4588	+	3.71099i	0.680099	+	0.144559i	0.145106	+	0.989416i	$0.453648\pi$
$660$	1.47719	−	8.16707i	0.0574994	−	0.317903i
$661$	−35.8685	+	7.62409i	−1.39512	+	0.296543i	−0.843311	−	0.537426i	$-0.819397\pi$
$661$	−35.8685	+	7.62409i	−1.39512	+	0.296543i	−0.551812	+	0.833968i	$0.686063\pi$
$662$	−22.2823	+	24.7470i	−0.866027	+	0.961820i
$663$	16.3916	−	57.5553i	0.636598	−	2.23526i
$664$	−53.0322	−	58.8983i	−2.05805	−	2.28570i
$665$	−12.9711	−	7.59656i	−0.502998	−	0.294582i
$666$	41.8760	−	35.3959i	1.62266	−	1.37156i
$667$	23.3603	−	16.9723i	0.904516	−	0.657169i
$668$	13.6786	−	23.6920i	0.529240	−	0.916670i
$669$	−17.1677	−	27.3642i	−0.663740	−	1.05796i
$670$	2.39764	+	0.795521i	0.0926290	+	0.0307337i
$671$	0.393881	−	3.74752i	0.0152056	−	0.144672i
$672$	−3.94076	−	0.687548i	−0.152018	−	0.0265227i
$673$	13.9358	+	15.4773i	0.537186	+	0.596606i	0.949240	−	0.314554i	$-0.101855\pi$
$673$	13.9358	+	15.4773i	0.537186	+	0.596606i	−0.412053	+	0.911160i	$0.635188\pi$
$674$	−29.9258			−1.15270
$675$	5.57962	−	25.3746i	0.214760	−	0.976667i
$676$	49.5070			1.90411
$677$	4.62872	+	5.14071i	0.177896	+	0.197574i	0.825498	−	0.564406i	$-0.190895\pi$
$677$	4.62872	+	5.14071i	0.177896	+	0.197574i	−0.647602	+	0.761979i	$0.724228\pi$
$678$	40.3726	+	7.04384i	1.55050	+	0.270517i
$679$	−1.08657	+	10.3381i	−0.0416989	+	0.396738i
$680$	−48.7426	−	67.9713i	−1.86919	−	2.60658i
$681$	15.6554	+	24.9538i	0.599917	+	0.956231i
$682$	0.980570	−	1.69840i	0.0375480	−	0.0650350i
$683$	25.6445	−	18.6318i	0.981258	−	0.712926i	0.0232689	−	0.999729i	$-0.492593\pi$
$683$	25.6445	−	18.6318i	0.981258	−	0.712926i	0.957989	+	0.286803i	$0.0925926\pi$
$684$	−11.5680	−	64.2511i	−0.442312	−	2.45670i
$685$	−17.6611	+	15.7048i	−0.674796	+	0.600050i
$686$	26.4411	+	29.3659i	1.00953	+	1.12119i
$687$	10.3291	−	36.2683i	0.394080	−	1.38372i
$688$	−14.1285	+	15.6912i	−0.538642	+	0.598223i
$689$	13.3448	−	2.83653i	0.508397	−	0.108063i
$690$	39.7308	−	5.40549i	1.51253	−	0.205784i
$691$	4.00894	+	0.852126i	0.152507	+	0.0324164i	0.283533	−	0.958963i	$-0.408494\pi$
$691$	4.00894	+	0.852126i	0.152507	+	0.0324164i	−0.131025	+	0.991379i	$0.541827\pi$
$692$	3.62934	−	2.63687i	0.137967	−	0.100239i
$693$	1.96763	+	0.269310i	0.0747440	+	0.0102302i
$694$	1.40496	−	1.02077i	0.0533317	−	0.0387478i
$695$	−0.548514	+	1.21169i	−0.0208063	+	0.0459622i
$696$	−41.5584	+	49.7088i	−1.57527	+	1.88421i
$697$	2.95109	−	28.0778i	0.111781	−	1.06352i
$698$	−42.0727	+	8.94283i	−1.59248	+	0.338491i
$699$	−14.6144	+	7.16051i	−0.552766	+	0.270835i
$700$	−8.62773	+	25.4735i	−0.326098	+	0.962808i
$701$	1.75231			0.0661838			0.0330919	−	0.999452i	$-0.489465\pi$
$701$	1.75231			0.0661838			0.0330919	+	0.999452i	$0.489465\pi$
$702$	−55.9226	−	31.8854i	−2.11066	−	1.20344i
$703$	−31.0370	−	22.5497i	−1.17058	−	0.850479i
$704$	2.66575	−	1.18687i	0.100469	−	0.0447319i
$705$	−11.8124	+	28.8701i	−0.444882	+	1.08731i
$706$	11.9846	+	5.33591i	0.451048	+	0.200820i
$707$	−10.0585	−	17.4218i	−0.378287	−	0.655213i
$708$	−11.7516	−	18.7314i	−0.441653	−	0.703968i
$709$	24.9030	+	5.29330i	0.935253	+	0.198794i	0.650239	−	0.759729i	$-0.274669\pi$
$709$	24.9030	+	5.29330i	0.935253	+	0.198794i	0.285013	+	0.958524i	$0.408002\pi$
$710$	−7.92606	−	4.64192i	−0.297460	−	0.174208i
$711$	−10.3009	+	0.757599i	−0.386314	+	0.0284122i
$712$	16.0981	+	49.5449i	0.603303	+	1.85677i
$713$	6.26488	+	1.33164i	0.234621	+	0.0498703i
$714$	30.2459	−	23.7185i	1.13192	−	0.887642i
$715$	−3.39435	+	4.61148i	−0.126941	+	0.172460i
$716$	−52.5971	+	58.4150i	−1.96564	+	2.18307i
$717$	−8.50534	+	0.312348i	−0.317638	+	0.0116649i
$718$	1.34655	−	2.33230i	0.0502530	−	0.0870407i
$719$	9.49736	−	6.90024i	0.354192	−	0.257335i	−0.396434	−	0.918063i	$-0.629752\pi$
$719$	9.49736	−	6.90024i	0.354192	−	0.257335i	0.750625	+	0.660728i	$0.229752\pi$
$720$	−31.5470	+	12.6504i	−1.17569	+	0.471453i
$721$	−15.8489	−	11.5149i	−0.590244	−	0.428838i
$722$	−18.6040	+	8.28303i	−0.692369	+	0.308262i
$723$	12.8351	+	5.15886i	0.477344	+	0.191860i
$724$	−30.0825	−	52.1045i	−1.11801	−	1.93645i
$725$	22.8623	+	26.0336i	0.849083	+	0.966864i
$726$	−41.4891	+	20.3281i	−1.53980	+	0.754448i
$727$	13.6361	+	15.1445i	0.505737	+	0.561677i	0.940905	−	0.338672i	$-0.109978\pi$
$727$	13.6361	+	15.1445i	0.505737	+	0.561677i	−0.435168	+	0.900349i	$0.643311\pi$
$728$	28.0725	+	20.3958i	1.04043	+	0.755920i
$729$	13.7518	+	23.2355i	0.509327	+	0.860573i
$730$	10.4846	−	47.8641i	0.388054	−	1.77153i
$731$	−3.01828	−	28.7170i	−0.111635	−	1.06214i
$732$	−47.6230	+	23.3335i	−1.76020	+	0.862432i
$733$	−39.6552	−	17.6556i	−1.46470	−	0.652125i	−0.489207	−	0.872168i	$-0.662714\pi$
$733$	−39.6552	−	17.6556i	−1.46470	−	0.652125i	−0.975490	+	0.220043i	$0.929380\pi$
$734$	−51.9238	+	57.6672i	−1.91654	+	2.12854i
$735$	19.8491	+	5.78635i	0.732145	+	0.213433i
$736$	−4.99566	−	5.54825i	−0.184143	−	0.204511i
$737$	0.0721606	+	0.222087i	0.00265807	+	0.00818069i
$738$	−28.5753	−	10.2841i	−1.05187	−	0.378565i
$739$	−2.42742	+	7.47084i	−0.0892942	+	0.274819i	−0.985725	−	0.168365i	$-0.946151\pi$
$739$	−2.42742	+	7.47084i	−0.0892942	+	0.274819i	0.896431	+	0.443184i	$0.146151\pi$
$740$	−28.3071	+	62.5317i	−1.04059	+	2.29871i
$741$	−12.3369	+	43.3182i	−0.453208	+	1.59133i
$742$	8.00505	+	3.56408i	0.293875	+	0.130841i
$743$	−16.6131	−	28.7747i	−0.609475	−	1.05564i	−0.991327	−	0.131418i	$-0.958047\pi$
$743$	−16.6131	−	28.7747i	−0.609475	−	1.05564i	0.381852	−	0.924223i	$-0.375286\pi$
$744$	−14.3621	+	0.527432i	−0.526541	+	0.0193366i
$745$	−4.51763	−	0.503179i	−0.165513	−	0.0184351i
$746$	−0.496906	−	0.361023i	−0.0181930	−	0.0132180i
$747$	10.5012	−	42.7737i	0.384219	−	1.56501i
$748$	4.58845	−	14.1218i	0.167770	−	0.516344i
$749$	6.89519	−	11.9428i	0.251945	−	0.436381i
$750$	10.8530	+	46.8724i	0.396295	+	1.71154i
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	−0.989871	−	0.141971i	$-0.954656\pi$
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	0.371985	−	0.928239i	$-0.378677\pi$
$752$	39.9163	−	8.48447i	1.45560	−	0.309397i
$753$	36.7019	+	6.40341i	1.33749	+	0.233353i
$754$	78.4256	−	34.9173i	2.85609	−	1.27161i
$755$	3.77306	+	8.61794i	0.137316	+	0.313639i
$756$	−11.5061	−	25.4718i	−0.418472	−	0.926402i
$757$	−9.25569			−0.336404			−0.168202	−	0.985753i	$-0.553796\pi$
$757$	−9.25569			−0.336404			−0.168202	+	0.985753i	$0.553796\pi$
$758$	−5.80147	−	55.1973i	−0.210719	−	2.00486i
$759$	2.57955	+	2.66160i	0.0936318	+	0.0966098i
$760$	36.6854	+	51.1576i	1.33072	+	1.85568i
$761$	−15.0763	+	3.20457i	−0.546517	+	0.116166i	−0.472892	−	0.881120i	$-0.656790\pi$
$761$	−15.0763	+	3.20457i	−0.546517	+	0.116166i	−0.0736245	+	0.997286i	$0.523457\pi$
$762$	−55.2180	+	13.8731i	−2.00034	+	0.502568i
$763$	16.7611	+	3.56268i	0.606792	+	0.128978i
$764$	−23.8752	+	73.4802i	−0.863773	+	2.65842i
$765$	16.0112	−	43.6367i	0.578886	−	1.57769i
$766$	−20.3600	−	62.6615i	−0.735636	−	2.26405i
$767$	1.59467	+	15.1722i	0.0575801	+	0.547838i
$768$	−46.8873	−	31.5032i	−1.69190	−	1.13677i
$769$	15.5474	+	6.92217i	0.560655	+	0.249620i	0.667441	−	0.744662i	$-0.267389\pi$
$769$	15.5474	+	6.92217i	0.560655	+	0.249620i	−0.106786	+	0.994282i	$0.534056\pi$
$770$	−3.50471	+	1.11476i	−0.126301	+	0.0401730i
$771$	5.72362	+	15.6378i	0.206131	+	0.563183i
$772$	20.5892	−	9.16689i	0.741020	−	0.329923i
$773$	8.95270	−	27.5536i	0.322006	−	0.991033i	−0.650768	−	0.759277i	$-0.725553\pi$
$773$	8.95270	−	27.5536i	0.322006	−	0.991033i	0.972774	−	0.231756i	$-0.0744471\pi$
$774$	−30.7741	−	4.21205i	−1.10615	−	0.151399i
$775$	−0.898098	+	7.63255i	−0.0322606	+	0.274169i
$776$	21.7665	−	37.7007i	0.781372	−	1.35338i
$777$	−15.2397	−	6.12536i	−0.546723	−	0.219746i
$778$	−3.37773	+	32.1370i	−0.121098	+	1.15217i
$779$	−2.22109	+	21.1323i	−0.0795790	+	0.757143i
$780$	80.3646	+	5.97537i	2.87751	+	0.213953i
$781$	−0.0887529	−	0.844428i	−0.00317583	−	0.0302160i
$782$	71.7360			2.56527
$783$	−35.8290	−	3.57020i	−1.28043	−	0.127589i
$784$	−8.35834	−	25.7243i	−0.298512	−	0.918726i
$785$	1.24054	+	0.138173i	0.0442768	+	0.00493161i
$786$	−6.08191	−	42.7167i	−0.216934	−	1.52366i
$787$	5.00153	−	5.55477i	0.178285	−	0.198006i	−0.647378	−	0.762169i	$-0.724134\pi$
$787$	5.00153	−	5.55477i	0.178285	−	0.198006i	0.825663	+	0.564163i	$0.190801\pi$
$788$	43.4993	−	48.3109i	1.54960	−	1.72100i
$789$	−15.5203	−	6.23811i	−0.552537	−	0.222083i
$790$	16.6237	−	9.46067i	0.591445	−	0.336595i
$791$	−3.79358	−	11.6754i	−0.134884	−	0.415130i
$792$	−7.06906	−	4.38192i	−0.251188	−	0.155705i
$793$	36.5877			1.29927
$794$	−7.98508	−	75.9729i	−0.283380	−	2.69618i
$795$	10.4999	−	1.42854i	0.372392	−	0.0506651i
$796$	7.47108	−	71.0826i	0.264805	−	2.51946i
$797$	−1.65961	+	15.7902i	−0.0587865	+	0.559317i	0.924999	+	0.379969i	$0.124065\pi$
$797$	−1.65961	+	15.7902i	−0.0587865	+	0.559317i	−0.983786	+	0.179348i	$0.942601\pi$
$798$	−22.7641	+	17.8514i	−0.805841	+	0.631932i
$799$	−27.9034	+	48.3301i	−0.987152	+	1.70980i
$800$	6.07647	−	6.58249i	0.214836	−	0.232726i
$801$	−17.7411	+	22.8770i	−0.626853	+	0.808318i
$802$	7.76865	−	23.9094i	0.274320	−	0.844271i
$803$	4.13782	−	1.84228i	0.146021	−	0.0650126i
$804$	2.10795	−	2.52136i	0.0743416	−	0.0889216i
$805$	−6.99945	−	9.76070i	−0.246698	−	0.344020i
$806$	17.3958	+	7.74511i	0.612741	+	0.272810i
$807$	28.2645	−	13.8486i	0.994957	−	0.487493i
$808$	8.80623	+	83.7857i	0.309802	+	2.94757i
$809$	−0.927281	−	2.85388i	−0.0326015	−	0.100337i	0.933432	−	0.358755i	$-0.116799\pi$
$809$	−0.927281	−	2.85388i	−0.0326015	−	0.100337i	−0.966033	+	0.258418i	$0.916799\pi$
$810$	−41.4797	−	27.9182i	−1.45745	−	0.980945i
$811$	−11.0539	+	34.0205i	−0.388156	+	1.19462i	0.546009	+	0.837779i	$0.316146\pi$
$811$	−11.0539	+	34.0205i	−0.388156	+	1.19462i	−0.934165	+	0.356841i	$0.883854\pi$
$812$	36.4589	+	7.74958i	1.27946	+	0.271957i
$813$	−3.01627	−	3.11220i	−0.105785	−	0.109150i
$814$	−9.18105	+	1.95149i	−0.321796	+	0.0683998i
$815$	−36.7734	−	12.2012i	−1.28812	−	0.427388i
$816$	−58.9757	+	14.8171i	−2.06456	+	0.518704i
$817$	2.27167	+	21.6135i	0.0794755	+	0.756159i
$818$	44.0028			1.53852
$819$	−0.603565	+	19.2737i	−0.0210903	+	0.673479i
$820$	37.8337	−	3.73931i	1.32121	−	0.130582i
$821$	−42.4446	+	18.8975i	−1.48133	+	0.659529i	−0.978760	−	0.205010i	$-0.934277\pi$
$821$	−42.4446	+	18.8975i	−1.48133	+	0.659529i	−0.502566	+	0.864539i	$0.667611\pi$
$822$	15.6331	+	42.7121i	0.545267	+	1.48976i
$823$	−40.1400	+	8.53203i	−1.39919	+	0.297408i	−0.844905	−	0.534917i	$-0.820343\pi$
$823$	−40.1400	+	8.53203i	−1.39919	+	0.297408i	−0.554289	+	0.832325i	$0.687010\pi$
$824$	41.0210	+	71.0504i	1.42903	+	2.47516i
$825$	−2.89475	+	3.37643i	−0.100782	+	0.117552i
$826$	−4.89927	+	8.48578i	−0.170467	+	0.295258i
$827$	12.0368	−	37.0454i	0.418560	−	1.28820i	−0.490468	−	0.871459i	$-0.663174\pi$
$827$	12.0368	−	37.0454i	0.418560	−	1.28820i	0.909028	−	0.416736i	$-0.136826\pi$
$828$	12.4373	−	50.6599i	0.432227	−	1.76055i
$829$	−4.44553	−	3.22987i	−0.154400	−	0.112178i	0.507903	−	0.861414i	$-0.330421\pi$
$829$	−4.44553	−	3.22987i	−0.154400	−	0.112178i	−0.662303	+	0.749236i	$0.730421\pi$
$830$	16.4625	+	79.8839i	0.571422	+	2.77281i
$831$	12.4015	+	19.7673i	0.430204	+	0.685720i
$832$	14.1666	+	24.5373i	0.491138	+	0.850677i
$833$	33.7916	+	15.0450i	1.17081	+	0.521279i
$834$	1.78143	+	1.83809i	0.0616860	+	0.0636479i
$835$	−12.7409	+	7.25096i	−0.440918	+	0.250930i
$836$	−3.45343	+	10.6286i	−0.119439	+	0.367596i
$837$	−4.72930	−	6.43592i	−0.163469	−	0.222458i
$838$	10.3078	+	31.7242i	0.356078	+	1.09590i
$839$	10.5199	+	11.6836i	0.363188	+	0.403362i	0.896849	−	0.442337i	$-0.145851\pi$
$839$	10.5199	+	11.6836i	0.363188	+	0.403362i	−0.533660	+	0.845699i	$0.679184\pi$
$840$	20.5695	+	17.4148i	0.709715	+	0.600867i
$841$	12.7251	−	14.1326i	0.438795	−	0.487331i
$842$	73.9958	+	32.9450i	2.55006	+	1.13536i
$843$	−0.0889851	+	1.30635i	−0.00306481	+	0.0449930i
$844$	6.31241	+	60.0586i	0.217282	+	2.06730i
$845$	−22.8921	−	13.4068i	−0.787512	−	0.461209i
$846$	43.3328	+	41.5454i	1.48981	+	1.42836i
$847$	11.1965	+	8.13473i	0.384716	+	0.279512i
$848$	−9.27606	−	10.3021i	−0.318541	−	0.353776i
$849$	−6.02059	−	4.04519i	−0.206626	−	0.138830i
$850$	7.93454	+	85.7100i	0.272153	+	2.93983i
$851$	−15.3270	−	26.5472i	−0.525403	−	0.910025i
$852$	−9.40323	+	7.37391i	−0.322149	+	0.252626i
$853$	1.27176	−	0.566226i	0.0435444	−	0.0193872i	−0.384849	−	0.922980i	$-0.625746\pi$
$853$	1.27176	−	0.566226i	0.0435444	−	0.0193872i	0.428393	+	0.903592i	$0.359080\pi$
$854$	19.0116	+	13.8127i	0.650564	+	0.472662i
$855$	−12.0506	+	32.8425i	−0.412122	+	1.12319i
$856$	−46.7227	+	33.9460i	−1.59695	+	1.16025i
$857$	−12.7340	+	22.0559i	−0.434985	+	0.753415i	−0.997294	−	0.0735113i	$-0.976580\pi$
$857$	−12.7340	+	22.0559i	−0.434985	+	0.753415i	0.562310	+	0.826927i	$0.309913\pi$
$858$	5.85638	+	9.33472i	0.199934	+	0.318682i
$859$	−4.28776	+	4.76204i	−0.146297	+	0.162479i	−0.811839	−	0.583881i	$-0.801533\pi$
$859$	−4.28776	+	4.76204i	−0.146297	+	0.162479i	0.665543	+	0.746360i	$0.268200\pi$
$860$	37.0544	−	11.7860i	1.26354	−	0.401900i
$861$	1.28230	+	9.00635i	0.0437008	+	0.306936i
$862$	−21.7628	−	4.62582i	−0.741243	−	0.157556i
$863$	−3.68829	−	11.3514i	−0.125551	−	0.386406i	0.868450	−	0.495777i	$-0.165117\pi$
$863$	−3.68829	−	11.3514i	−0.125551	−	0.386406i	−0.994001	+	0.109370i	$0.965117\pi$
$864$	0.0502928	+	9.30969i	0.00171100	+	0.316722i
$865$	−2.39229	+	0.236443i	−0.0813404	+	0.00803931i
$866$	−67.7386	−	14.3983i	−2.30185	−	0.489273i
$867$	25.1315	−	47.4716i	0.853512	−	1.61222i
$868$	4.13386	+	7.16006i	0.140312	+	0.243028i
$869$	1.61524	+	0.719151i	0.0547933	+	0.0243955i
$870$	62.7572	−	22.5293i	2.12767	−	0.763814i
$871$	−2.07135	+	0.922224i	−0.0701850	+	0.0312484i
$872$	−58.0563	−	42.1804i	−1.96603	−	1.42841i
$873$	24.1270	−	1.77446i	0.816576	−	0.0600565i
$874$	−53.9910			−1.82627
$875$	10.8879	−	9.44254i	0.368077	−	0.319216i
$876$	−52.9116	−	35.5509i	−1.78772	−	1.20115i
$877$	0.819396	−	0.174168i	0.0276690	−	0.00588123i	−0.194056	−	0.980990i	$-0.562164\pi$
$877$	0.819396	−	0.174168i	0.0276690	−	0.00588123i	0.221725	+	0.975109i	$0.428831\pi$
$878$	−0.816658	+	7.76998i	−0.0275609	+	0.262224i
$879$	−15.5982	−	42.6169i	−0.526115	−	1.43743i
$880$	5.78256	+	0.644069i	0.194930	+	0.0217116i
$881$	−8.77572	+	6.37593i	−0.295661	+	0.214811i	−0.725720	−	0.687991i	$-0.758493\pi$
$881$	−8.77572	+	6.37593i	−0.295661	+	0.214811i	0.430058	+	0.902801i	$0.358493\pi$
$882$	24.3838	−	31.4426i	0.821046	−	1.05873i
$883$	−29.2715	+	21.2670i	−0.985064	+	0.715691i	−0.958835	−	0.283965i	$-0.908350\pi$
$883$	−29.2715	+	21.2670i	−0.985064	+	0.715691i	−0.0262292	+	0.999656i	$0.508350\pi$
$884$	141.024	+	29.9756i	4.74316	+	1.00819i
$885$	0.361385	+	11.8438i	0.0121478	+	0.398126i
$886$	−47.9579	+	10.1938i	−1.61118	+	0.342466i
$887$	−30.3562	+	33.7140i	−1.01926	+	1.13201i	−0.0280658	+	0.999606i	$0.508935\pi$
$887$	−30.3562	+	33.7140i	−1.01926	+	1.13201i	−0.991196	+	0.132399i	$0.957732\pi$
$888$	47.8708	+	49.3933i	1.60644	+	1.65753i
$889$	11.4117	+	12.6740i	0.382738	+	0.425073i
$890$	11.4715	−	52.3694i	0.384526	−	1.75543i
$891$	−0.194570	−	4.61784i	−0.00651833	−	0.154703i
$892$	62.9620	−	45.7446i	2.10812	−	1.53164i
$893$	21.0011	−	36.3750i	0.702775	−	1.21724i
$894$	−4.09299	+	7.73135i	−0.136890	+	0.258575i
$895$	40.1401	−	12.7675i	1.34174	−	0.426772i
$896$	−2.38503	+	22.6920i	−0.0796782	+	0.758088i
$897$	−23.0836	+	27.6108i	−0.770740	+	0.921898i
$898$	22.8965	+	25.4291i	0.764066	+	0.848581i
$899$	10.6509			0.355226
$900$	61.9040	+	9.25671i	2.06347	+	0.308557i
$901$	18.9581			0.631585
$902$	3.47864	+	3.86342i	0.115826	+	0.128638i
$903$	3.19800	+	8.73744i	0.106423	+	0.290764i
$904$	−5.37397	+	51.1299i	−0.178736	+	1.70055i
$905$	−0.200027	+	32.2398i	−0.00664912	+	1.07169i
$906$	18.0929	−	0.664440i	0.601097	−	0.0220746i
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	−0.968606	−	0.248602i	$-0.920029\pi$
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	0.699599	+	0.714536i	$0.253362\pi$
$908$	−57.4159	+	41.7151i	−1.90541	+	1.38436i
$909$	−35.7560	+	30.2229i	−1.18595	+	1.00243i
$910$	−14.3217	−	32.7118i	−0.474760	−	1.08439i
$911$	−9.27545	−	10.3014i	−0.307309	−	0.341302i	0.569631	−	0.821900i	$-0.307086\pi$
$911$	−9.27545	−	10.3014i	−0.307309	−	0.341302i	−0.876941	+	0.480599i	$0.840419\pi$
$912$	44.3872	−	11.1519i	1.46981	−	0.369277i
$913$	−5.04494	+	5.60298i	−0.166963	+	0.185431i
$914$	−39.0474	+	8.29977i	−1.29157	+	0.274532i
$915$	28.3398	+	2.10716i	0.936886	+	0.0696606i
$916$	88.8658	+	18.8890i	2.93621	+	0.624111i
$917$	−10.4564	+	7.59702i	−0.345301	+	0.250876i
$918$	−66.7991	−	59.4960i	−2.20470	−	1.96366i
$919$	33.8071	−	24.5623i	1.11519	−	0.810236i	0.131720	−	0.991287i	$-0.457950\pi$
$919$	33.8071	−	24.5623i	1.11519	−	0.810236i	0.983474	+	0.181051i	$0.0579500\pi$
$920$	10.1526	+	49.2653i	0.334722	+	1.62423i
$921$	23.3158	+	4.06793i	0.768282	+	0.134043i
$922$	2.66667	−	25.3717i	0.0878221	−	0.835571i
$923$	8.06414	−	1.71409i	0.265434	−	0.0564198i
$924$	−0.325159	+	4.77350i	−0.0106969	+	0.157037i
$925$	30.0232	−	21.2490i	0.987157	−	0.698663i
$926$	−44.7769			−1.47146
$927$	−19.8387	+	41.0499i	−0.651587	+	1.34825i
$928$	−10.0442	−	7.29755i	−0.329718	−	0.239554i
$929$	−28.4644	+	12.6732i	−0.933888	+	0.415794i	−0.816535	−	0.577297i	$-0.804108\pi$
$929$	−28.4644	+	12.6732i	−0.933888	+	0.415794i	−0.117353	+	0.993090i	$0.537441\pi$
$930$	13.0282	+	7.00100i	0.427213	+	0.229572i
$931$	−25.4328	−	11.3234i	−0.833526	−	0.371110i
$932$	−19.6038	−	33.9548i	−0.642145	−	1.11223i
$933$	−1.65359	+	0.0607261i	−0.0541361	+	0.00198808i
$934$	−85.8314	−	18.2440i	−2.80849	−	0.596963i
$935$	−5.94598	+	5.28736i	−0.194454	+	0.172915i
$936$	35.1393	−	72.7098i	1.14857	−	2.37659i
$937$	−11.2706	−	34.6872i	−0.368193	−	1.13318i	−0.947957	−	0.318398i	$-0.896855\pi$
$937$	−11.2706	−	34.6872i	−0.368193	−	1.13318i	0.579764	−	0.814784i	$-0.303145\pi$
$938$	−1.42447	−	0.302780i	−0.0465106	−	0.00988613i
$939$	19.2625	+	7.74225i	0.628609	+	0.252659i
$940$	−71.3264	−	23.6656i	−2.32641	−	0.771887i
$941$	10.4003	−	11.5507i	0.339041	−	0.376543i	−0.549380	−	0.835573i	$-0.685136\pi$
$941$	10.4003	−	11.5507i	0.339041	−	0.376543i	0.888421	+	0.459029i	$0.151803\pi$
$942$	1.12394	−	2.12303i	0.0366198	−	0.0691720i
$943$	−8.48922	+	14.7038i	−0.276447	+	0.478820i
$944$	12.5412	−	9.11169i	0.408180	−	0.296560i
$945$	−1.57752	+	14.8941i	−0.0513166	+	0.484506i
$946$	4.30163	+	3.12532i	0.139858	+	0.101613i
$947$	−14.8544	+	6.61361i	−0.482704	+	0.214914i	−0.633637	−	0.773630i	$-0.718439\pi$
$947$	−14.8544	+	6.61361i	−0.482704	+	0.214914i	0.150933	+	0.988544i	$0.451772\pi$
$948$	−3.50751	−	24.6353i	−0.113919	−	0.800117i
$949$	21.9896	+	38.0871i	0.713813	+	1.23636i
$950$	−5.97182	−	64.5084i	−0.193751	−	2.09293i
$951$	0.265752	−	3.90138i	0.00861760	−	0.126511i
$952$	32.2641	+	35.8329i	1.04569	+	1.16135i
$953$	29.6469	+	21.5397i	0.960357	+	0.697741i	0.953234	−	0.302234i	$-0.0977324\pi$
$953$	29.6469	+	21.5397i	0.960357	+	0.697741i	0.00712369	+	0.999975i	$0.497732\pi$
$954$	4.86226	−	19.8050i	0.157421	−	0.641212i
$955$	30.9388	−	27.5118i	1.00116	−	0.890261i
$956$	−2.14332	−	20.3924i	−0.0693200	−	0.659536i
$957$	5.11613	+	3.43748i	0.165381	+	0.111118i
$958$	3.87900	+	1.72704i	0.125325	+	0.0557981i
$959$	9.11654	−	10.1249i	0.294389	−	0.326952i
$960$	9.55989	+	19.8217i	0.308544	+	0.639744i
$961$	−19.1622	−	21.2818i	−0.618136	−	0.686510i
$962$	−28.1628	−	86.6762i	−0.908006	−	2.79455i
$963$	−30.1980	−	10.8682i	−0.973118	−	0.350222i
$964$	−10.2984	+	31.6953i	−0.331690	+	1.02084i
$965$	−12.0029	−	1.33690i	−0.386388	−	0.0430363i
$966$	−22.4184	+	5.63243i	−0.721300	+	0.181220i
$967$	−37.2631	−	16.5906i	−1.19830	−	0.533517i	−0.292108	−	0.956385i	$-0.594357\pi$
$967$	−37.2631	−	16.5906i	−1.19830	−	0.533517i	−0.906191	+	0.422868i	$0.861023\pi$
$968$	−28.9793	−	50.1937i	−0.931431	−	1.61329i
$969$	−29.2837	+	55.3147i	−0.940728	+	1.77696i
$970$	−38.9364	+	22.1590i	−1.25017	+	0.711482i
$971$	36.3301	+	26.3954i	1.16589	+	0.847068i	0.990511	−	0.137433i	$-0.0438852\pi$
$971$	36.3301	+	26.3954i	1.16589	+	0.847068i	0.175378	+	0.984501i	$0.443885\pi$
$972$	−53.5974	+	36.8583i	−1.71914	+	1.18223i
$973$	0.236941	−	0.729230i	0.00759599	−	0.0233780i
$974$	40.6362	−	70.3840i	1.30207	−	2.25525i
$975$	−35.5426	−	24.5263i	−1.13827	−	0.785470i
$976$	−18.5888	−	32.1967i	−0.595011	−	1.03059i
$977$	6.51932	−	1.38572i	0.208571	−	0.0443332i	−0.102441	−	0.994739i	$-0.532665\pi$
$977$	6.51932	−	1.38572i	0.208571	−	0.0443332i	0.311012	+	0.950406i	$0.399332\pi$
$978$	−47.8260	+	57.2056i	−1.52931	+	1.82923i
$979$	4.52730	−	2.01568i	0.144693	−	0.0644215i
$980$	−10.6583	+	48.6568i	−0.340466	+	1.55429i
$981$	1.24822	−	39.8598i	0.0398528	−	1.27263i
$982$	−102.522			−3.27161
$983$	3.26978	+	31.1098i	0.104290	+	0.992250i	0.914081	+	0.405532i	$0.132914\pi$
$983$	3.26978	+	31.1098i	0.104290	+	0.992250i	−0.809791	+	0.586718i	$0.800420\pi$
$984$	10.4352	−	36.6409i	0.332663	−	1.16807i
$985$	−33.1971	+	10.5591i	−1.05775	+	0.336442i
$986$	116.686	−	24.8023i	3.71603	−	0.789867i
$987$	4.92547	−	17.2946i	0.156779	−	0.550494i
$988$	−106.140	−	22.5607i	−3.37676	−	0.717751i
$989$	−5.36608	+	16.5151i	−0.170632	+	0.525150i
$990$	3.99858	+	7.56769i	0.127083	+	0.240517i
$991$	−1.60963	−	4.95394i	−0.0511317	−	0.157367i	0.922230	−	0.386641i	$-0.126365\pi$
$991$	−1.60963	−	4.95394i	−0.0511317	−	0.157367i	−0.973362	+	0.229274i	$0.926365\pi$
$992$	−0.287859	−	2.73880i	−0.00913953	−	0.0869568i
$993$	1.57769	−	23.1613i	0.0500665	−	0.735002i
$994$	4.83737	+	2.15374i	0.153432	+	0.0683124i
$995$	−22.7043	+	30.8455i	−0.719774	+	0.977868i
$996$	104.530	+	18.2375i	3.31217	+	0.577878i
$997$	−20.9597	+	9.33186i	−0.663800	+	0.295543i	−0.710844	−	0.703350i	$-0.751687\pi$
$997$	−20.9597	+	9.33186i	−0.663800	+	0.295543i	0.0470436	+	0.998893i	$0.485020\pi$
$998$	2.67071	−	8.21961i	0.0845399	−	0.260187i
$999$	−7.74532	+	37.4320i	−0.245051	+	1.18430i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.196.2	yes	224
3.2	odd	2		675.2.r.a.46.27		224
9.4	even	3	inner	225.2.q.a.121.27	yes	224
9.5	odd	6		675.2.r.a.496.2		224
25.6	even	5	inner	225.2.q.a.106.27	yes	224
75.56	odd	10		675.2.r.a.181.2		224
225.31	even	15	inner	225.2.q.a.31.2	✓	224
225.131	odd	30		675.2.r.a.631.27		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.2	✓	224	225.31	even	15	inner
225.2.q.a.106.27	yes	224	25.6	even	5	inner
225.2.q.a.121.27	yes	224	9.4	even	3	inner
225.2.q.a.196.2	yes	224	1.1	even	1	trivial
675.2.r.a.46.27		224	3.2	odd	2
675.2.r.a.181.2		224	75.56	odd	10
675.2.r.a.496.2		224	9.5	odd	6
675.2.r.a.631.27		224	225.131	odd	30

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

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Newspace parameters

Newform invariants

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$q$ -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	225.2.q.a.196.2

Level	$225$
Weight	$2$
Character	225.196
Analytic conductor	$1.797$
Analytic rank	$0$
Dimension	$224$
Inner twists	$4$