LMFDB - Embedded newform 945.2.cs.b.209.129

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			209.129
Character	$\chi$	$=$	945.209
Dual form			945.2.cs.b.104.129

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.39005 - 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(0.644408 - 2.14120i) q^{5} +(0.473977 + 4.37980i) q^{6} +(1.18021 - 2.36793i) q^{7} +(3.14000 - 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +O(q^{10})$	\(q+(2.39005 - 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(0.644408 - 2.14120i) q^{5} +(0.473977 + 4.37980i) q^{6} +(1.18021 - 2.36793i) q^{7} +(3.14000 - 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +(-0.322477 - 5.67816i) q^{10} +(0.730141 + 0.128744i) q^{11} +(3.41471 + 6.94681i) q^{12} +(-4.21165 - 1.53292i) q^{13} +(0.760868 - 6.68616i) q^{14} +(3.33457 + 1.96994i) q^{15} +(1.22155 - 6.92774i) q^{16} +(1.33497 - 0.770744i) q^{17} +(-7.56246 - 1.01538i) q^{18} +(2.23093 + 1.28803i) q^{19} +(-3.94483 - 9.18163i) q^{20} +(3.49417 + 2.96492i) q^{21} +(1.85707 - 0.327452i) q^{22} +(-3.69844 + 3.10336i) q^{23} +(7.84769 + 7.53185i) q^{24} +(-4.16948 - 2.75961i) q^{25} -11.3996 q^{26} +(3.44108 - 3.89345i) q^{27} +(-2.76185 - 11.4970i) q^{28} +(1.66423 + 4.57243i) q^{29} +(9.68346 + 1.80750i) q^{30} +(5.24901 + 6.25553i) q^{31} +(-0.925915 - 5.25112i) q^{32} +(-0.518696 + 1.17473i) q^{33} +(2.52017 - 3.00342i) q^{34} +(-4.30969 - 4.05297i) q^{35} +(-13.0969 + 2.86825i) q^{36} +(-4.43022 + 2.55779i) q^{37} +(6.45249 + 1.13775i) q^{38} +(4.32115 - 6.44913i) q^{39} +(-9.62177 - 10.2281i) q^{40} +(7.73911 + 2.81680i) q^{41} +(10.9305 + 4.04671i) q^{42} +(9.27186 + 1.63488i) q^{43} +(2.86949 - 1.65670i) q^{44} +(-4.69320 + 4.79311i) q^{45} +(-6.13983 + 10.6345i) q^{46} +(-0.190266 + 0.226750i) q^{47} +(11.1461 + 4.92150i) q^{48} +(-4.21423 - 5.58930i) q^{49} +(-12.3659 - 2.96857i) q^{50} +(0.743834 + 2.56423i) q^{51} +(-18.8223 + 6.85075i) q^{52} +7.21473 q^{53} +(4.83742 - 12.2990i) q^{54} +(0.746175 - 1.48041i) q^{55} +(-9.17249 - 13.8540i) q^{56} +(-3.08956 + 3.21912i) q^{57} +(7.95519 + 9.48063i) q^{58} +(-1.47111 - 8.34311i) q^{59} +(17.0750 - 2.83499i) q^{60} +(2.03914 - 2.43015i) q^{61} +(17.9872 + 10.3849i) q^{62} +(-6.43270 + 4.64978i) q^{63} +(0.253630 + 0.439300i) q^{64} +(-5.99631 + 8.03017i) q^{65} +(-0.217801 + 3.25889i) q^{66} +(-4.52044 + 12.4198i) q^{67} +(2.35619 - 6.47359i) q^{68} +(-3.68891 - 7.50465i) q^{69} +(-13.8261 - 5.93779i) q^{70} +(-0.774450 + 0.447129i) q^{71} +(-15.9154 + 10.0819i) q^{72} +(-7.05268 + 12.2156i) q^{73} +(-8.36341 + 9.96713i) q^{74} +(6.36686 - 5.87053i) q^{75} +(11.3377 - 1.99914i) q^{76} +(1.16657 - 1.57698i) q^{77} +(4.71764 - 19.1728i) q^{78} +(14.0134 - 5.10046i) q^{79} +(-14.0465 - 7.07987i) q^{80} +(5.12426 + 7.39878i) q^{81} +20.9472 q^{82} +(-2.88480 - 7.92592i) q^{83} +(20.4796 + 0.112856i) q^{84} +(-0.790052 - 3.35511i) q^{85} +(23.5824 - 4.15822i) q^{86} +(-8.37903 + 0.906769i) q^{87} +(2.99283 - 3.56672i) q^{88} +(-3.71773 + 6.43929i) q^{89} +(-7.04744 + 15.5384i) q^{90} +(-8.60046 + 8.16377i) q^{91} +(-3.74674 + 21.2488i) q^{92} +(-12.6933 + 6.23942i) q^{93} +(-0.257494 + 0.707458i) q^{94} +(4.19555 - 3.94684i) q^{95} +(9.21497 + 0.615862i) q^{96} +(0.473281 - 2.68411i) q^{97} +(-14.9344 - 9.69273i) q^{98} +(-1.76110 - 1.35854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	2.39005	−	0.869908i	1.69002	−	0.615118i	0.695394	−	0.718628i	$-0.255230\pi$
$2$	2.39005	−	0.869908i	1.69002	−	0.615118i	0.994628	+	0.103510i	$0.0330075\pi$
$3$	−0.413843	+	1.68188i	−0.238933	+	0.971036i
$3$	−0.413843	+	1.68188i	−0.238933	+	0.971036i
$4$	3.42352	−	2.87268i	1.71176	−	1.43634i
$5$	0.644408	−	2.14120i	0.288188	−	0.957574i
$5$	0.644408	−	2.14120i	0.288188	−	0.957574i
$6$	0.473977	+	4.37980i	0.193500	+	1.78804i
$7$	1.18021	−	2.36793i	0.446076	−	0.894995i
$7$	1.18021	−	2.36793i	0.446076	−	0.894995i
$8$	3.14000	−	5.43864i	1.11016	−	1.92285i
$9$	−2.65747	−	1.39207i	−0.885822	−	0.464024i
$10$	−0.322477	−	5.67816i	−0.101976	−	1.79559i
$11$	0.730141	+	0.128744i	0.220146	+	0.0388176i	0.282633	−	0.959228i	$-0.408792\pi$
$11$	0.730141	+	0.128744i	0.220146	+	0.0388176i	−0.0624872	+	0.998046i	$0.519903\pi$
$12$	3.41471	+	6.94681i	0.985741	+	2.00537i
$13$	−4.21165	−	1.53292i	−1.16810	−	0.425155i	−0.316117	−	0.948720i	$-0.602379\pi$
$13$	−4.21165	−	1.53292i	−1.16810	−	0.425155i	−0.851985	+	0.523565i	$0.824602\pi$
$14$	0.760868	−	6.68616i	0.203350	−	1.78695i
$15$	3.33457	+	1.96994i	0.860981	+	0.508637i
$16$	1.22155	−	6.92774i	0.305387	−	1.73193i
$17$	1.33497	−	0.770744i	0.323777	−	0.186933i	−0.329298	−	0.944226i	$-0.606812\pi$
$17$	1.33497	−	0.770744i	0.323777	−	0.186933i	0.653075	+	0.757293i	$0.273479\pi$
$18$	−7.56246	−	1.01538i	−1.78249	−	0.239327i
$19$	2.23093	+	1.28803i	0.511809	+	0.295493i	0.733577	−	0.679606i	$-0.237849\pi$
$19$	2.23093	+	1.28803i	0.511809	+	0.295493i	−0.221768	+	0.975100i	$0.571183\pi$
$20$	−3.94483	−	9.18163i	−0.882091	−	2.05307i
$21$	3.49417	+	2.96492i	0.762491	+	0.646999i
$22$	1.85707	−	0.327452i	0.395929	−	0.0698129i
$23$	−3.69844	+	3.10336i	−0.771178	+	0.647095i	−0.941010	−	0.338378i	$-0.890122\pi$
$23$	−3.69844	+	3.10336i	−0.771178	+	0.647095i	0.169833	+	0.985473i	$0.445677\pi$
$24$	7.84769	+	7.53185i	1.60190	+	1.53743i
$25$	−4.16948	−	2.75961i	−0.833895	−	0.551923i
$26$	−11.3996			−2.23564
$27$	3.44108	−	3.89345i	0.662236	−	0.749295i
$28$	−2.76185	−	11.4970i	−0.521941	−	2.17273i
$29$	1.66423	+	4.57243i	0.309040	+	0.849079i	0.992845	+	0.119414i	$0.0381017\pi$
$29$	1.66423	+	4.57243i	0.309040	+	0.849079i	−0.683805	+	0.729665i	$0.739676\pi$
$30$	9.68346	+	1.80750i	1.76795	+	0.330003i
$31$	5.24901	+	6.25553i	0.942750	+	1.12353i	0.992188	+	0.124749i	$0.0398125\pi$
$31$	5.24901	+	6.25553i	0.942750	+	1.12353i	−0.0494381	+	0.998777i	$0.515743\pi$
$32$	−0.925915	−	5.25112i	−0.163680	−	0.928276i
$33$	−0.518696	+	1.17473i	−0.0902933	+	0.204495i
$34$	2.52017	−	3.00342i	0.432205	−	0.515082i
$35$	−4.30969	−	4.05297i	−0.728470	−	0.685077i
$36$	−13.0969	+	2.86825i	−2.18281	+	0.478042i
$37$	−4.43022	+	2.55779i	−0.728323	+	0.420498i	−0.817808	−	0.575491i	$-0.804811\pi$
$37$	−4.43022	+	2.55779i	−0.728323	+	0.420498i	0.0894853	+	0.995988i	$0.471478\pi$
$38$	6.45249	+	1.13775i	1.04673	+	0.184567i
$39$	4.32115	−	6.44913i	0.691938	−	1.03269i
$40$	−9.62177	−	10.2281i	−1.52133	−	1.61720i
$41$	7.73911	+	2.81680i	1.20865	+	0.439911i	0.866234	−	0.499639i	$-0.166534\pi$
$41$	7.73911	+	2.81680i	1.20865	+	0.439911i	0.342412	+	0.939550i	$0.388756\pi$
$42$	10.9305	+	4.04671i	1.68661	+	0.624422i
$43$	9.27186	+	1.63488i	1.41395	+	0.249317i	0.827861	−	0.560933i	$-0.189557\pi$
$43$	9.27186	+	1.63488i	1.41395	+	0.249317i	0.586085	+	0.810250i	$0.300669\pi$
$44$	2.86949	−	1.65670i	0.432592	−	0.249757i
$45$	−4.69320	+	4.79311i	−0.699621	+	0.714514i
$46$	−6.13983	+	10.6345i	−0.905268	+	1.56797i
$47$	−0.190266	+	0.226750i	−0.0277531	+	0.0330749i	−0.779742	−	0.626100i	$-0.784650\pi$
$47$	−0.190266	+	0.226750i	−0.0277531	+	0.0330749i	0.751989	+	0.659175i	$0.229094\pi$
$48$	11.1461	+	4.92150i	1.60880	+	0.710357i
$49$	−4.21423	−	5.58930i	−0.602033	−	0.798471i
$50$	−12.3659	−	2.96857i	−1.74880	−	0.419819i
$51$	0.743834	+	2.56423i	0.104158	+	0.359064i
$52$	−18.8223	+	6.85075i	−2.61018	+	0.950028i
$53$	7.21473			0.991019			0.495510	−	0.868602i	$-0.334981\pi$
$53$	7.21473			0.991019			0.495510	+	0.868602i	$0.334981\pi$
$54$	4.83742	−	12.2990i	0.658290	−	1.67368i
$55$	0.746175	−	1.48041i	0.100614	−	0.199619i
$56$	−9.17249	−	13.8540i	−1.22573	−	1.85132i
$57$	−3.08956	+	3.21912i	−0.409223	+	0.426382i
$58$	7.95519	+	9.48063i	1.04457	+	1.24487i
$59$	−1.47111	−	8.34311i	−0.191523	−	1.08618i	−0.917284	−	0.398233i	$-0.869623\pi$
$59$	−1.47111	−	8.34311i	−0.191523	−	1.08618i	0.725761	−	0.687947i	$-0.241488\pi$
$60$	17.0750	−	2.83499i	2.20437	−	0.365996i
$61$	2.03914	−	2.43015i	0.261085	−	0.311148i	−0.619538	−	0.784967i	$-0.712680\pi$
$61$	2.03914	−	2.43015i	0.261085	−	0.311148i	0.880623	+	0.473818i	$0.157125\pi$
$62$	17.9872	+	10.3849i	2.28437	+	1.31888i
$63$	−6.43270	+	4.64978i	−0.810443	+	0.585817i
$64$	0.253630	+	0.439300i	0.0317037	+	0.0549125i
$65$	−5.99631	+	8.03017i	−0.743750	+	0.996020i
$66$	−0.217801	+	3.25889i	−0.0268094	+	0.401142i
$67$	−4.52044	+	12.4198i	−0.552259	+	1.51732i	0.278359	+	0.960477i	$0.410209\pi$
$67$	−4.52044	+	12.4198i	−0.552259	+	1.51732i	−0.830618	+	0.556842i	$0.812013\pi$
$68$	2.35619	−	6.47359i	0.285731	−	0.785038i
$69$	−3.68891	−	7.50465i	−0.444093	−	0.903453i
$70$	−13.8261	−	5.93779i	−1.65253	−	0.709701i
$71$	−0.774450	+	0.447129i	−0.0919103	+	0.0530644i	−0.545251	−	0.838273i	$-0.683566\pi$
$71$	−0.774450	+	0.447129i	−0.0919103	+	0.0530644i	0.453340	+	0.891337i	$0.350232\pi$
$72$	−15.9154	+	10.0819i	−1.87565	+	1.18816i
$73$	−7.05268	+	12.2156i	−0.825454	+	1.42973i	0.0761186	+	0.997099i	$0.475747\pi$
$73$	−7.05268	+	12.2156i	−0.825454	+	1.42973i	−0.901572	+	0.432629i	$0.857586\pi$
$74$	−8.36341	+	9.96713i	−0.972227	+	1.15866i
$75$	6.36686	−	5.87053i	0.735182	−	0.677870i
$76$	11.3377	−	1.99914i	1.30052	−	0.229318i
$77$	1.16657	−	1.57698i	0.132943	−	0.179714i
$78$	4.71764	−	19.1728i	0.534167	−	2.17089i
$79$	14.0134	−	5.10046i	1.57663	−	0.573846i	0.602161	−	0.798374i	$-0.294306\pi$
$79$	14.0134	−	5.10046i	1.57663	−	0.573846i	0.974468	+	0.224528i	$0.0720841\pi$
$80$	−14.0465	−	7.07987i	−1.57045	−	0.791554i
$81$	5.12426	+	7.39878i	0.569363	+	0.822086i
$82$	20.9472			2.31324
$83$	−2.88480	−	7.92592i	−0.316648	−	0.869983i	−0.991273	−	0.131823i	$-0.957917\pi$
$83$	−2.88480	−	7.92592i	−0.316648	−	0.869983i	0.674625	−	0.738160i	$-0.264305\pi$
$84$	20.4796	+	0.112856i	2.23451	+	0.0123136i
$85$	−0.790052	−	3.35511i	−0.0856932	−	0.363912i
$86$	23.5824	−	4.15822i	2.54296	−	0.448392i
$87$	−8.37903	+	0.906769i	−0.898326	+	0.0972159i
$88$	2.99283	−	3.56672i	0.319037	−	0.380213i
$89$	−3.71773	+	6.43929i	−0.394078	+	0.682564i	−0.992983	−	0.118257i	$-0.962269\pi$
$89$	−3.71773	+	6.43929i	−0.394078	+	0.682564i	0.598905	+	0.800820i	$0.295603\pi$
$90$	−7.04744	+	15.5384i	−0.742865	+	1.63789i
$91$	−8.60046	+	8.16377i	−0.901574	+	0.855795i
$92$	−3.74674	+	21.2488i	−0.390625	+	2.21535i
$93$	−12.6933	+	6.23942i	−1.31624	+	0.646998i
$94$	−0.257494	+	0.707458i	−0.0265584	+	0.0729687i
$95$	4.19555	−	3.94684i	0.430454	−	0.404938i
$96$	9.21497	+	0.615862i	0.940498	+	0.0628561i
$97$	0.473281	−	2.68411i	0.0480544	−	0.272530i	−0.951308	−	0.308243i	$-0.900259\pi$
$97$	0.473281	−	2.68411i	0.0480544	−	0.272530i	0.999362	+	0.0357128i	$0.0113702\pi$
$98$	−14.9344	−	9.69273i	−1.50860	−	0.979113i
$99$	−1.76110	−	1.35854i	−0.176998	−	0.136539i
$100$	−22.2018	+	2.52995i	−2.22018	+	0.252995i
$101$	−3.99029	−	3.34825i	−0.397048	−	0.333163i	0.422303	−	0.906455i	$-0.361222\pi$
$101$	−3.99029	−	3.34825i	−0.397048	−	0.333163i	−0.819351	+	0.573292i	$0.805666\pi$
$102$	4.00844	+	5.48157i	0.396895	+	0.542756i
$103$	−1.83483	−	10.4059i	−0.180792	−	1.02532i	−0.931244	−	0.364396i	$-0.881276\pi$
$103$	−1.83483	−	10.4059i	−0.180792	−	1.02532i	0.750453	−	0.660924i	$-0.229836\pi$
$104$	−21.5616	+	18.0923i	−2.11428	+	1.77410i
$105$	8.60017	−	5.57110i	0.839290	−	0.543684i
$106$	17.2436	−	6.27615i	1.67485	−	0.609594i
$107$	−14.1118			−1.36424			−0.682122	−	0.731238i	$-0.738943\pi$
$107$	−14.1118			−1.36424			−0.682122	+	0.731238i	$0.738943\pi$
$108$	0.595993	−	23.2144i	0.0573495	−	2.23381i
$109$	−5.85360			−0.560673			−0.280337	−	0.959902i	$-0.590446\pi$
$109$	−5.85360			−0.560673			−0.280337	+	0.959902i	$0.590446\pi$
$110$	0.495572	−	4.18737i	0.0472510	−	0.399250i
$111$	−2.46848	−	8.50963i	−0.234298	−	0.807699i
$112$	−14.9628	−	11.0687i	−1.41385	−	1.04589i
$113$	−2.41576	−	13.7004i	−0.227255	−	1.28883i	−0.858326	−	0.513104i	$-0.828495\pi$
$113$	−2.41576	−	13.7004i	−0.227255	−	1.28883i	0.631071	−	0.775725i	$-0.282616\pi$
$114$	−4.58388	+	10.3815i	−0.429320	+	0.972316i
$115$	4.26161	+	9.91893i	0.397397	+	0.924945i
$116$	18.8327	+	10.8730i	1.74857	+	1.00954i
$117$	9.05840	+	9.93661i	0.837449	+	0.918640i
$118$	−10.7738	−	18.6607i	−0.991807	−	1.71786i
$119$	−0.249535	−	4.07075i	−0.0228749	−	0.373165i
$120$	21.1843	−	11.9499i	1.93386	−	1.09087i
$121$	−9.82009	−	3.57422i	−0.892735	−	0.324929i
$122$	2.75964	−	7.58204i	0.249846	−	0.686446i
$123$	−7.94032	+	11.8506i	−0.715954	+	1.06853i
$124$	35.9402	+	6.33723i	3.22753	+	0.569100i
$125$	−8.59573	+	7.14936i	−0.768826	+	0.639458i
$126$	−11.3296	+	16.7091i	−1.00932	+	1.48856i
$127$	−5.83188	−	3.36704i	−0.517496	−	0.298776i	0.218414	−	0.975856i	$-0.429912\pi$
$127$	−5.83188	−	3.36704i	−0.517496	−	0.298776i	−0.735909	+	0.677080i	$0.763245\pi$
$128$	9.15764	+	7.68417i	0.809429	+	0.679191i
$129$	−6.58678	+	14.9176i	−0.579933	+	1.31342i
$130$	−7.34598	+	24.4088i	−0.644285	+	2.14079i
$131$	3.66473	−	3.07508i	0.320189	−	0.268671i	−0.468499	−	0.883464i	$-0.655205\pi$
$131$	3.66473	−	3.07508i	0.320189	−	0.268671i	0.788688	+	0.614793i	$0.210761\pi$
$132$	1.59886	+	5.51177i	0.139163	+	0.479738i
$133$	5.68291	−	3.76255i	0.492771	−	0.326255i
$134$			33.6163i			2.90401i
$135$	−6.11920	−	9.87702i	−0.526657	−	0.850078i
$136$		−	9.68053i		−	0.830099i
$137$	−11.5492	+	4.20355i	−0.986711	+	0.359133i	−0.784446	−	0.620198i	$-0.787052\pi$
$137$	−11.5492	+	4.20355i	−0.986711	+	0.359133i	−0.202265	+	0.979331i	$0.564830\pi$
$138$	−15.3451	−	14.7275i	−1.30626	−	1.25369i
$139$	0.986486	+	1.17565i	0.0836727	+	0.0997172i	0.806257	−	0.591566i	$-0.201490\pi$
$139$	0.986486	+	1.17565i	0.0836727	+	0.0997172i	−0.722584	+	0.691283i	$0.757046\pi$
$140$	−26.3972	−	1.49511i	−2.23097	−	0.126360i
$141$	−0.302627	−	0.413844i	−0.0254858	−	0.0348519i
$142$	−1.46202	+	1.74236i	−0.122690	+	0.146216i
$143$	−2.87775	−	1.66147i	−0.240649	−	0.138939i
$144$	−12.8901	+	16.7098i	−1.07418	+	1.39248i
$145$	10.8629	−	0.616934i	0.902118	−	0.0512335i
$146$	−6.22983	+	35.3311i	−0.515584	+	2.92402i
$147$	11.1446	−	4.77475i	0.919190	−	0.393815i
$148$	−7.81926	+	21.4832i	−0.642739	+	1.76591i
$149$	3.68673	−	10.1292i	0.302029	−	0.829817i	−0.692118	−	0.721784i	$-0.743322\pi$
$149$	3.68673	−	10.1292i	0.302029	−	0.829817i	0.994147	−	0.108033i	$-0.0344553\pi$
$150$	10.1103	−	19.5695i	0.825504	−	1.59784i
$151$	−0.0756148	+	0.428833i	−0.00615344	+	0.0348979i	−0.987730	−	0.156172i	$-0.950085\pi$
$151$	−0.0756148	+	0.428833i	−0.00615344	+	0.0348979i	0.981576	+	0.191070i	$0.0611957\pi$
$152$	14.0102	−	8.08879i	1.13638	−	0.656088i
$153$	−4.62056	+	0.189854i	−0.373550	+	0.0153488i
$154$	1.41634	−	4.78388i	0.114132	−	0.385496i
$155$	16.7768	−	7.20807i	1.34755	−	0.578966i
$156$	−3.73269	−	34.4920i	−0.298854	−	2.76157i
$157$	2.90797	+	16.4919i	0.232081	+	1.31620i	0.848675	+	0.528915i	$0.177401\pi$
$157$	2.90797	+	16.4919i	0.232081	+	1.31620i	−0.616594	+	0.787281i	$0.711488\pi$
$158$	29.0558	−	24.3807i	2.31156	−	1.93963i
$159$	−2.98577	+	12.1343i	−0.236787	+	0.962316i
$160$	−11.8404	−	1.40130i	−0.936064	−	0.110782i
$161$	2.98363	+	12.4203i	0.235143	+	0.978854i
$162$	18.6835	+	13.2258i	1.46792	+	1.03912i
$163$			12.8858i			1.00929i	0.863326	+	0.504646i	$0.168377\pi$
$163$			12.8858i			1.00929i	−0.863326	+	0.504646i	$0.831623\pi$
$164$	34.5868	−	12.5886i	2.70078	−	0.983002i
$165$	2.18109	+	1.86764i	0.169797	+	0.145395i
$166$	−13.7897	−	16.4339i	−1.07028	−	1.27552i
$167$	−10.2701	+	1.81089i	−0.794722	+	0.140131i	−0.556246	−	0.831017i	$-0.687759\pi$
$167$	−10.2701	+	1.81089i	−0.794722	+	0.140131i	−0.238476	+	0.971148i	$0.576648\pi$
$168$	27.0968	−	9.69367i	2.09057	−	0.747883i
$169$	5.42962	+	4.55599i	0.417663	+	0.350461i
$170$	−4.80690	−	7.33161i	−0.368672	−	0.562309i
$171$	−4.13558	−	6.52850i	−0.316256	−	0.499247i
$172$	36.4389	−	21.0380i	2.77844	−	1.60413i
$173$	−14.4406	−	2.54627i	−1.09790	−	0.193589i	−0.404782	−	0.914413i	$-0.632653\pi$
$173$	−14.4406	−	2.54627i	−1.09790	−	0.193589i	−0.693118	+	0.720824i	$0.743764\pi$
$174$	−19.2375	+	9.45621i	−1.45839	+	0.716874i
$175$	−11.4554	+	6.61613i	−0.865949	+	0.500133i
$176$	1.78380	−	4.90096i	0.134459	−	0.369424i
$177$	14.6409	+	0.978496i	1.10048	+	0.0735482i
$178$	−3.28397	+	18.6243i	−0.246144	+	1.39595i
$179$	−6.16591	+	3.55989i	−0.460862	+	0.266079i	−0.712407	−	0.701767i	$-0.752395\pi$
$179$	−6.16591	+	3.55989i	−0.460862	+	0.266079i	0.251545	+	0.967846i	$0.419061\pi$
$180$	−2.29824	+	29.8914i	−0.171301	+	2.22797i
$181$	17.4008	+	10.0463i	1.29339	+	0.746739i	0.979254	−	0.202639i	$-0.0649518\pi$
$181$	17.4008	+	10.0463i	1.29339	+	0.746739i	0.314136	+	0.949378i	$0.398285\pi$
$182$	−13.4538	+	26.9934i	−0.997265	+	2.00089i
$183$	3.24334	+	4.43529i	0.239755	+	0.327866i
$184$	5.26495	+	29.8590i	0.388137	+	2.20123i
$185$	2.62186	+	11.1342i	0.192763	+	0.818606i
$186$	−24.9100	+	25.9546i	−1.82649	+	1.90308i
$187$	1.07394	−	0.390883i	0.0785344	−	0.0285842i
$188$			1.32286i			0.0964792i
$189$	−5.15826	−	12.7433i	−0.375208	−	0.926941i
$190$	6.59419	−	13.0829i	0.478393	−	0.949134i
$191$	2.42277	+	6.65652i	0.175306	+	0.481649i	0.995962	−	0.0897733i	$-0.0286143\pi$
$191$	2.42277	+	6.65652i	0.175306	+	0.481649i	−0.820656	+	0.571422i	$0.806392\pi$
$192$	−0.843815	+	0.244775i	−0.0608971	+	0.0176651i
$193$	0.593111	+	0.706843i	0.0426931	+	0.0508796i	0.786968	−	0.616993i	$-0.211649\pi$
$193$	0.593111	+	0.706843i	0.0426931	+	0.0508796i	−0.744275	+	0.667873i	$0.767205\pi$
$194$	−1.20376	−	6.82688i	−0.0864251	−	0.490141i
$195$	−11.0243	−	13.4083i	−0.789465	−	0.960190i
$196$	−30.4838	−	7.02897i	−2.17741	−	0.502069i
$197$	3.64955	−	6.32121i	0.260020	−	0.450368i	−0.706227	−	0.707985i	$-0.749604\pi$
$197$	3.64955	−	6.32121i	0.260020	−	0.450368i	0.966247	+	0.257618i	$0.0829376\pi$
$198$	−5.39094	−	1.71499i	−0.383117	−	0.121879i
$199$	−7.77362	+	4.48810i	−0.551057	+	0.318153i	−0.749548	−	0.661950i	$-0.769729\pi$
$199$	−7.77362	+	4.48810i	−0.551057	+	0.318153i	0.198491	+	0.980103i	$0.436396\pi$
$200$	−28.1007	+	14.0111i	−1.98702	+	0.990732i
$201$	−19.0179	−	12.7427i	−1.34142	−	0.898801i
$202$	−12.4497	−	4.53131i	−0.875955	−	0.318822i
$203$	12.7914	+	1.45562i	0.897777	+	0.102165i
$204$	9.91273	+	6.64190i	0.694030	+	0.465026i
$205$	11.0185	−	14.7558i	0.769565	−	1.03059i
$206$	−13.4375	−	23.2744i	−0.936235	−	1.62161i
$207$	14.1486	−	3.09858i	0.983394	−	0.215366i
$208$	−15.7644	+	27.3047i	−1.09306	+	1.89324i
$209$	1.46306	+	1.22766i	0.101202	+	0.0849188i
$210$	15.7085	−	20.7966i	1.08399	−	1.43510i
$211$	−0.598558	−	3.39459i	−0.0412064	−	0.233693i	0.957248	−	0.289268i	$-0.0934120\pi$
$211$	−0.598558	−	3.39459i	−0.0412064	−	0.233693i	−0.998455	+	0.0555749i	$0.982301\pi$
$212$	24.6998	−	20.7256i	1.69639	−	1.42344i
$213$	−0.431518	−	1.48758i	−0.0295671	−	0.101927i
$214$	−33.7281	+	12.2760i	−2.30560	+	0.839171i
$215$	9.47547	−	18.7994i	0.646222	−	1.28211i
$216$	−10.3701	−	30.9402i	−0.705594	−	2.10521i
$217$	21.0076	−	5.04651i	1.42609	−	0.342579i
$218$	−13.9904	+	5.09210i	−0.947551	+	0.344880i
$219$	−17.6265	−	16.9171i	−1.19109	−	1.14315i
$220$	−1.69821	−	7.21175i	−0.114493	−	0.486216i
$221$	−6.80391	+	1.19971i	−0.457680	+	0.0807014i
$222$	−13.3024	−	18.1911i	−0.892799	−	1.22091i
$223$	−3.87043	−	3.24767i	−0.259183	−	0.217480i	0.503932	−	0.863744i	$-0.331886\pi$
$223$	−3.87043	−	3.24767i	−0.259183	−	0.217480i	−0.763115	+	0.646263i	$0.776331\pi$
$224$	−13.5271	−	4.00490i	−0.903817	−	0.267589i
$225$	7.23866	+	13.1378i	0.482577	+	0.875853i
$226$	−17.6919	−	30.6433i	−1.17685	−	2.03836i
$227$	−13.0401	−	2.29932i	−0.865503	−	0.152611i	−0.276767	−	0.960937i	$-0.589263\pi$
$227$	−13.0401	−	2.29932i	−0.865503	−	0.152611i	−0.588736	+	0.808326i	$0.700374\pi$
$228$	−1.32971	+	19.8960i	−0.0880621	+	1.31765i
$229$	−6.84571	+	18.8084i	−0.452377	+	1.24290i	0.478670	+	0.877995i	$0.341119\pi$
$229$	−6.84571	+	18.8084i	−0.452377	+	1.24290i	−0.931047	+	0.364900i	$0.881103\pi$
$230$	18.8140	+	19.9996i	1.24056	+	1.31873i
$231$	2.16952	+	2.61466i	0.142744	+	0.172032i
$232$	30.0935	+	5.30629i	1.97573	+	0.348375i
$233$	−13.3489	−	23.1211i	−0.874519	−	1.51471i	−0.857275	−	0.514860i	$-0.827844\pi$
$233$	−13.3489	−	23.1211i	−0.874519	−	1.51471i	−0.0172442	−	0.999851i	$-0.505489\pi$
$234$	30.2940	+	15.8690i	1.98038	+	1.03739i
$235$	0.362908	+	0.553517i	0.0236735	+	0.0361074i
$236$	−29.0035	−	24.3368i	−1.88796	−	1.58419i
$237$	2.77903	+	25.6797i	0.180517	+	1.66807i
$238$	−4.13758	−	9.51224i	−0.268200	−	0.616587i
$239$	−15.6258	−	18.6221i	−1.01075	−	1.20456i	−0.978746	−	0.205075i	$-0.934256\pi$
$239$	−15.6258	−	18.6221i	−1.01075	−	1.20456i	−0.0320019	−	0.999488i	$-0.510188\pi$
$240$	17.7206	−	20.6946i	1.14386	−	1.33583i
$241$	−1.41743	−	3.89436i	−0.0913047	−	0.250858i	0.885632	−	0.464388i	$-0.153726\pi$
$241$	−1.41743	−	3.89436i	−0.0913047	−	0.250858i	−0.976936	+	0.213531i	$0.931504\pi$
$242$	−26.5798			−1.70861
$243$	−14.5645	+	5.55648i	−0.934315	+	0.356448i
$244$		−	14.1774i		−	0.907618i
$245$	−14.6835	+	5.42172i	−0.938094	+	0.346381i
$246$	−8.66888	+	35.2308i	−0.552707	+	2.24624i
$247$	−7.42145	−	8.84454i	−0.472216	−	0.562765i
$248$	50.5034	−	8.90512i	3.20697	−	0.565475i
$249$	14.5243	−	1.57181i	0.920443	−	0.0996093i
$250$	−14.3250	+	24.5649i	−0.905991	+	1.55362i
$251$	7.75081	−	13.4248i	0.489227	−	0.847365i	−0.510697	−	0.859761i	$-0.670612\pi$
$251$	7.75081	−	13.4248i	0.489227	−	0.847365i	0.999923	+	0.0123956i	$0.00394575\pi$
$252$	−8.66518	+	34.3977i	−0.545855	+	2.16685i
$253$	−3.09992	+	1.78974i	−0.194890	+	0.112520i
$254$	−16.8675	−	2.97420i	−1.05836	−	0.186618i
$255$	5.96986	+	0.0597123i	0.373847	+	0.00373933i
$256$	27.6184	+	10.0523i	1.72615	+	0.628268i
$257$	9.65902	−	26.5379i	0.602513	−	1.65539i	−0.143650	−	0.989629i	$-0.545884\pi$
$257$	9.65902	−	26.5379i	0.602513	−	1.65539i	0.746163	−	0.665763i	$-0.231894\pi$
$258$	−2.76579	+	41.3838i	−0.172191	+	2.57644i
$259$	0.828107	+	13.5092i	0.0514561	+	0.839419i
$260$	2.53959	+	44.7169i	0.157499	+	2.77323i
$261$	1.94253	−	14.4678i	0.120239	−	0.895535i
$262$	6.08387	−	10.5376i	0.375863	−	0.651014i
$263$	5.36619	+	4.50276i	0.330893	+	0.277652i	0.793064	−	0.609139i	$-0.208485\pi$
$263$	5.36619	+	4.50276i	0.330893	+	0.277652i	−0.462171	+	0.886791i	$0.652929\pi$
$264$	4.76024	+	6.50965i	0.292972	+	0.400641i
$265$	4.64923	−	15.4482i	0.285600	−	0.948974i
$266$	10.3094	−	13.9363i	0.632109	−	0.854490i
$267$	−9.29159	−	8.91765i	−0.568636	−	0.545751i
$268$	20.2022	+	55.5052i	1.23405	+	3.39052i
$269$	23.6685			1.44309			0.721546	−	0.692366i	$-0.243432\pi$
$269$	23.6685			1.44309			0.721546	+	0.692366i	$0.243432\pi$
$270$	−23.2173	−	18.2835i	−1.41296	−	1.11270i
$271$			3.15216i			0.191480i	0.995406	+	0.0957399i	$0.0305217\pi$
$271$			3.15216i			0.191480i	−0.995406	+	0.0957399i	$0.969478\pi$
$272$	−3.70879	−	10.1898i	−0.224878	−	0.617848i
$273$	−10.1713	−	17.8435i	−0.615593	−	1.07994i
$274$	−23.9464	+	20.0934i	−1.44665	+	1.21389i
$275$	−2.68902	−	2.55170i	−0.162154	−	0.153873i
$276$	−34.1875	−	15.0953i	−2.05785	−	0.908629i
$277$	2.11219	−	2.51722i	0.126909	−	0.151245i	−0.698848	−	0.715270i	$-0.746304\pi$
$277$	2.11219	−	2.51722i	0.126909	−	0.151245i	0.825757	+	0.564025i	$0.190748\pi$
$278$	3.38046	+	1.95171i	0.202747	+	0.117056i
$279$	−5.24092	−	23.9309i	−0.313766	−	1.43270i
$280$	−35.5751	+	10.7125i	−2.12602	+	0.640194i
$281$	29.4169	+	5.18700i	1.75487	+	0.309431i	0.956281	−	0.292449i	$-0.0944703\pi$
$281$	29.4169	+	5.18700i	1.75487	+	0.309431i	0.798587	+	0.601880i	$0.205581\pi$
$282$	−1.08330	−	0.725851i	−0.0645096	−	0.0432238i
$283$	5.05630	+	1.84034i	0.300566	+	0.109397i	0.487901	−	0.872899i	$-0.337763\pi$
$283$	5.05630	+	1.84034i	0.300566	+	0.109397i	−0.187335	+	0.982296i	$0.559985\pi$
$284$	−1.36689	+	3.75550i	−0.0811100	+	0.222848i
$285$	4.90183	+	8.68980i	0.290359	+	0.514739i
$286$	−8.32329	−	1.46762i	−0.492167	−	0.0867823i
$287$	15.8037	−	15.0013i	0.932866	−	0.885498i
$288$	−4.84936	+	15.2436i	−0.285751	+	0.898240i
$289$	−7.31191	+	12.6646i	−0.430112	+	0.744976i
$290$	25.4263	−	10.9243i	1.49308	−	0.641495i
$291$	4.31850	+	1.90681i	0.253155	+	0.111779i
$292$	10.9465	+	62.0805i	0.640593	+	3.63298i
$293$	14.8565	+	17.7053i	0.867926	+	1.03435i	0.999075	+	0.0429915i	$0.0136888\pi$
$293$	14.8565	+	17.7053i	0.867926	+	1.03435i	−0.131149	+	0.991363i	$0.541867\pi$
$294$	22.4825	−	21.1067i	1.31121	−	1.23097i
$295$	−18.8123	−	2.22642i	−1.09529	−	0.129627i
$296$			32.1258i			1.86727i
$297$	3.01373	−	2.39975i	0.174874	−	0.139248i
$298$		−	27.4165i		−	1.58819i
$299$	20.3337	−	7.40087i	1.17593	−	0.428004i
$300$	4.93298	−	38.3878i	0.284806	−	2.21632i
$301$	14.8140	−	20.0257i	0.853864	−	1.15426i
$302$	0.192322	+	1.09071i	0.0110669	+	0.0627633i
$303$	7.28272	−	5.32555i	0.418381	−	0.305945i
$304$	11.6483	−	13.8819i	0.668075	−	0.796181i
$305$	−3.88940	−	5.93220i	−0.222706	−	0.339677i
$306$	−10.8782	+	4.47323i	−0.621867	+	0.255717i
$307$	−10.5131	−	18.2093i	−0.600017	−	1.03926i	−0.992818	−	0.119636i	$-0.961827\pi$
$307$	−10.5131	−	18.2093i	−0.600017	−	1.03926i	0.392801	−	0.919624i	$-0.371506\pi$
$308$	−0.536373	−	8.75002i	−0.0305627	−	0.498579i
$309$	18.2608	+	1.22042i	1.03882	+	0.0694272i
$310$	33.8272	−	31.8220i	1.92126	−	1.80737i
$311$	18.6776	+	6.79811i	1.05911	+	0.385485i	0.812095	−	0.583526i	$-0.198327\pi$
$311$	18.6776	+	6.79811i	1.05911	+	0.385485i	0.247018	+	0.969011i	$0.420549\pi$
$312$	−21.5060	−	43.7514i	−1.21754	−	2.47694i
$313$	−3.83618	+	21.7561i	−0.216834	+	1.22973i	0.660862	+	0.750508i	$0.270191\pi$
$313$	−3.83618	+	21.7561i	−0.216834	+	1.22973i	−0.877696	+	0.479219i	$0.840920\pi$
$314$	21.2966	+	36.8868i	1.20184	+	2.08165i
$315$	5.81082	+	16.7700i	0.327403	+	0.944885i
$316$	33.3232	−	57.7175i	1.87458	−	3.24686i
$317$	3.01300	+	2.52821i	0.169227	+	0.141998i	0.723468	−	0.690358i	$-0.242547\pi$
$317$	3.01300	+	2.52821i	0.169227	+	0.141998i	−0.554241	+	0.832356i	$0.686991\pi$
$318$	3.41961	+	31.5991i	0.191762	+	1.77199i
$319$	0.626451	+	3.55278i	0.0350745	+	0.198917i
$320$	1.10407	−	0.259984i	0.0617194	−	0.0145335i
$321$	5.84010	−	23.7345i	0.325962	−	1.32473i
$322$	17.9355	+	27.0896i	0.999508	+	1.50964i
$323$	3.97095			0.220950
$324$	38.7974	+	10.6095i	2.15541	+	0.589419i
$325$	13.3301	+	18.0140i	0.739423	+	0.999237i
$326$	11.2095	+	30.7977i	0.620834	+	1.70573i
$327$	2.42247	−	9.84508i	0.133963	−	0.544434i
$328$	39.6204	−	33.2454i	2.18767	−	1.83567i
$329$	0.312376	+	0.718148i	0.0172219	+	0.0395928i
$330$	6.83758	+	2.56641i	0.376397	+	0.141276i
$331$	−27.7622	−	23.2952i	−1.52595	−	1.28042i	−0.820469	−	0.571691i	$-0.806288\pi$
$331$	−27.7622	−	23.2952i	−1.52595	−	1.28042i	−0.705479	−	0.708731i	$-0.749268\pi$
$332$	−32.6448	−	18.8475i	−1.79162	−	1.03439i
$333$	15.3338	−	0.630048i	0.840286	−	0.0345264i
$334$	−22.9707	+	13.2621i	−1.25690	+	0.725672i
$335$	23.6803	+	17.6826i	1.29379	+	0.966102i
$336$	24.8085	−	20.5849i	1.35342	−	1.12300i
$337$	−0.198807	+	0.546218i	−0.0108297	+	0.0297544i	−0.944990	−	0.327100i	$-0.893929\pi$
$337$	−0.198807	+	0.546218i	−0.0108297	+	0.0297544i	0.934160	+	0.356854i	$0.116151\pi$
$338$	16.9404	+	6.16579i	0.921435	+	0.335375i
$339$	24.0423	+	1.60681i	1.30580	+	0.0872702i
$340$	−12.3429	−	9.21672i	−0.669388	−	0.499847i
$341$	3.02716	+	5.24319i	0.163930	+	0.283935i
$342$	−15.5635	−	12.0059i	−0.841575	−	0.649203i
$343$	−18.2088	+	3.38250i	−0.983180	+	0.182638i
$344$	38.0051	−	45.2928i	2.04910	−	2.44202i
$345$	−18.4461	+	3.06264i	−0.993106	+	0.164887i
$346$	−36.7289	+	6.47629i	−1.97456	+	0.348168i
$347$	26.3941	−	22.1472i	1.41691	−	1.18893i	0.463934	−	0.885870i	$-0.346437\pi$
$347$	26.3941	−	22.1472i	1.41691	−	1.18893i	0.952973	−	0.303056i	$-0.0980071\pi$
$348$	−26.0810	+	27.1746i	−1.39809	+	1.45671i
$349$	4.81070	+	13.2173i	0.257511	+	0.707505i	0.999319	+	0.0368933i	$0.0117462\pi$
$349$	4.81070	+	13.2173i	0.257511	+	0.707505i	−0.741808	+	0.670612i	$0.766032\pi$
$350$	−21.6236	+	25.7781i	−1.15583	+	1.37790i
$351$	−20.4610	+	11.1230i	−1.09213	+	0.593701i
$352$		−	3.95327i		−	0.210710i
$353$	−11.5048	−	31.6091i	−0.612337	−	1.68238i	−0.724999	−	0.688750i	$-0.758160\pi$
$353$	−11.5048	−	31.6091i	−0.612337	−	1.68238i	0.112662	−	0.993633i	$-0.464062\pi$
$354$	35.8438	−	10.3976i	1.90508	−	0.552627i
$355$	0.458330	+	1.94639i	0.0243256	+	0.103303i
$356$	5.77029	+	32.7249i	0.305824	+	1.73442i
$357$	6.94980	+	1.26496i	0.367822	+	0.0669490i
$358$	−11.6401	+	13.8721i	−0.615197	+	0.733163i
$359$	−25.4663	−	14.7030i	−1.34406	−	0.775993i	−0.356658	−	0.934235i	$-0.616084\pi$
$359$	−25.4663	−	14.7030i	−1.34406	−	0.775993i	−0.987400	+	0.158242i	$0.949417\pi$
$360$	11.3313	+	40.5750i	0.597212	+	2.13849i
$361$	−6.18198	−	10.7075i	−0.325367	−	0.563553i
$362$	50.3282	+	8.87422i	2.64519	+	0.466418i
$363$	10.0754	−	15.0371i	0.528821	−	0.789242i
$364$	−5.99203	+	52.6552i	−0.314068	+	2.75988i
$365$	21.6112	+	22.9730i	1.13118	+	1.20246i
$366$	11.6101	+	7.77917i	0.606867	+	0.406624i
$367$	1.05874	−	6.00442i	0.0552658	−	0.313428i	−0.944626	−	0.328149i	$-0.893575\pi$
$367$	1.05874	−	6.00442i	0.0552658	−	0.313428i	0.999892	+	0.0147214i	$0.00468614\pi$
$368$	16.9814	+	29.4127i	0.885219	+	1.53324i
$369$	−16.6452	−	18.2590i	−0.866516	−	0.950524i
$370$	15.9522	+	24.3306i	0.829313	+	1.26489i
$371$	8.51486	−	17.0840i	0.442070	−	0.886958i
$372$	−25.5321	+	57.8247i	−1.32378	+	2.99807i
$373$	12.4167	−	2.18941i	0.642914	−	0.113363i	0.157320	−	0.987548i	$-0.449714\pi$
$373$	12.4167	−	2.18941i	0.642914	−	0.113363i	0.485594	+	0.874185i	$0.338603\pi$
$374$	2.22675	−	1.86846i	0.115142	−	0.0966159i
$375$	−8.46711	−	17.4157i	−0.437240	−	0.899345i
$376$	0.635776	+	1.74678i	0.0327876	+	0.0900833i
$377$		−	21.8086i		−	1.12320i
$378$	−23.4140	−	25.9700i	−1.20429	−	1.33575i
$379$	2.16560			0.111239			0.0556196	−	0.998452i	$-0.482287\pi$
$379$	2.16560			0.111239			0.0556196	+	0.998452i	$0.482287\pi$
$380$	3.02555	−	25.5646i	0.155207	−	1.31143i
$381$	8.07645	−	8.41512i	0.413769	−	0.431120i
$382$	11.5811	+	13.8018i	0.592541	+	0.706163i
$383$	9.24695	−	1.63049i	0.472497	−	0.0833140i	0.0676710	−	0.997708i	$-0.478443\pi$
$383$	9.24695	−	1.63049i	0.472497	−	0.0833140i	0.404826	+	0.914394i	$0.367332\pi$
$384$	−16.7137	+	12.2220i	−0.852918	+	0.623703i
$385$	−2.62488	−	3.51409i	−0.133777	−	0.179094i
$386$	2.03246	+	1.17344i	0.103449	+	0.0597265i
$387$	−22.3638	−	17.2518i	−1.13682	−	0.876956i
$388$	−6.09030	−	10.5487i	−0.309188	−	0.535529i
$389$	−5.08968	−	0.897448i	−0.258057	−	0.0455024i	0.0431227	−	0.999070i	$-0.486269\pi$
$389$	−5.08968	−	0.897448i	−0.258057	−	0.0455024i	−0.301180	+	0.953567i	$0.597380\pi$
$390$	−38.0126	−	22.4565i	−1.92484	−	1.13713i
$391$	−2.54540	+	6.99343i	−0.128726	+	0.353673i
$392$	−43.6308	+	5.36928i	−2.20369	+	0.271190i
$393$	3.65530	+	7.43626i	0.184385	+	0.375109i
$394$	3.22375	−	18.2828i	0.162410	−	0.921074i
$395$	−1.89075	−	33.2922i	−0.0951340	−	1.67511i
$396$	−9.93184	+	0.408088i	−0.499094	+	0.0205072i
$397$	−13.8639	+	24.0130i	−0.695808	+	1.20518i	0.274099	+	0.961701i	$0.411620\pi$
$397$	−13.8639	+	24.0130i	−0.695808	+	1.20518i	−0.969907	+	0.243474i	$0.921713\pi$
$398$	−14.6751	+	17.4891i	−0.735597	+	0.876651i
$399$	3.97634	+	11.1151i	0.199066	+	0.556451i
$400$	−24.2111	+	25.5140i	−1.21056	+	1.27570i
$401$	22.1510	+	26.3985i	1.10617	+	1.31828i	0.943415	+	0.331614i	$0.107593\pi$
$401$	22.1510	+	26.3985i	1.10617	+	1.31828i	0.162753	+	0.986667i	$0.447963\pi$
$402$	−56.5388	−	13.9119i	−2.81990	−	0.693862i
$403$	−12.5178	−	34.3924i	−0.623557	−	1.71321i
$404$	−23.2793			−1.15819
$405$	19.1444	−	6.20424i	0.951292	−	0.308291i
$406$	31.8383	−	7.64829i	1.58011	−	0.379578i
$407$	−3.56398	+	1.29718i	−0.176660	+	0.0642990i
$408$	16.2815	+	4.00623i	0.806056	+	0.198338i
$409$	20.7578	+	24.7382i	1.02641	+	1.22323i	0.974456	+	0.224577i	$0.0720999\pi$
$409$	20.7578	+	24.7382i	1.02641	+	1.22323i	0.0519522	+	0.998650i	$0.483456\pi$
$410$	13.4986	−	44.8522i	0.666647	−	2.21509i
$411$	−2.29034	−	21.1639i	−0.112974	−	1.04394i
$412$	−36.1743	−	30.3538i	−1.78218	−	1.49543i
$413$	−21.4922	−	6.36308i	−1.05756	−	0.313106i
$414$	31.1204	−	19.7137i	1.52948	−	0.968877i
$415$	−18.8300	+	1.06940i	−0.924327	+	0.0524949i
$416$	−4.14990	+	23.5353i	−0.203466	+	1.15391i
$417$	−2.38555	+	1.17262i	−0.116821	+	0.0574235i
$418$	4.56475	+	1.66143i	0.223269	+	0.0812634i
$419$	−20.3282	−	7.39884i	−0.993095	−	0.361457i	−0.206177	−	0.978515i	$-0.566102\pi$
$419$	−20.3282	−	7.39884i	−0.993095	−	0.361457i	−0.786918	+	0.617058i	$0.788325\pi$
$420$	13.4389	−	43.7783i	0.655752	−	2.13616i
$421$	−5.24056	+	29.7207i	−0.255409	+	1.44850i	0.539611	+	0.841915i	$0.318571\pi$
$421$	−5.24056	+	29.7207i	−0.255409	+	1.44850i	−0.795020	+	0.606583i	$0.792540\pi$
$422$	−4.38357	−	7.59256i	−0.213389	−	0.369600i
$423$	0.821277	−	0.337717i	0.0399319	−	0.0164203i
$424$	22.6542	−	39.2383i	1.10019	−	1.90558i
$425$	−7.69307	−	0.470399i	−0.373169	−	0.0228177i
$426$	−2.32540	−	3.18000i	−0.112666	−	0.154072i
$427$	−3.34783	−	7.69661i	−0.162013	−	0.372465i
$428$	−48.3123	+	40.5388i	−2.33526	+	1.95952i
$429$	3.98533	−	4.15245i	0.192414	−	0.200482i
$430$	6.29314	−	53.1743i	0.303482	−	2.56429i
$431$		−	22.6738i		−	1.09216i	−0.837734	−	0.546078i	$-0.816120\pi$
$431$		−	22.6738i		−	1.09216i	0.837734	−	0.546078i	$-0.183880\pi$
$432$	−22.7694	−	28.5949i	−1.09549	−	1.37578i
$433$	−16.0559			−0.771599			−0.385799	−	0.922583i	$-0.626074\pi$
$433$	−16.0559			−0.771599			−0.385799	+	0.922583i	$0.626074\pi$
$434$	45.8193	−	30.3361i	2.19940	−	1.45618i
$435$	−3.45794	+	18.5255i	−0.165796	+	0.888230i
$436$	−20.0399	+	16.8155i	−0.959739	+	0.805317i
$437$	−12.2481	+	2.15968i	−0.585908	+	0.103311i
$438$	−56.8446	−	25.0994i	−2.71614	−	1.19930i
$439$	2.84928	−	3.39564i	0.135989	−	0.162065i	−0.693752	−	0.720214i	$-0.744044\pi$
$439$	2.84928	−	3.39564i	0.135989	−	0.162065i	0.829741	+	0.558149i	$0.188488\pi$
$440$	−5.70845	−	8.70667i	−0.272139	−	0.415074i
$441$	3.41847	+	20.7199i	0.162784	+	0.986662i
$442$	−15.2181	+	8.78615i	−0.723849	+	0.417915i
$443$	−0.934802	+	5.30152i	−0.0444138	+	0.251883i	−0.998928	−	0.0462809i	$-0.985263\pi$
$443$	−0.934802	+	5.30152i	−0.0444138	+	0.251883i	0.954515	+	0.298164i	$0.0963742\pi$
$444$	−32.8964	−	22.0418i	−1.56119	−	1.04606i
$445$	11.3921	+	12.1099i	0.540036	+	0.574066i
$446$	−12.0757	−	4.39520i	−0.571801	−	0.208119i
$447$	15.5104	+	10.3926i	0.733618	+	0.491551i
$448$	1.33957	−	0.0821150i	0.0632887	−	0.00387957i
$449$	−15.2817	+	8.82291i	−0.721190	+	0.416379i	−0.815190	−	0.579193i	$-0.803368\pi$
$449$	−15.2817	+	8.82291i	−0.721190	+	0.416379i	0.0940008	+	0.995572i	$0.470034\pi$
$450$	28.7295	+	25.1031i	1.35432	+	1.18337i
$451$	5.28799	+	3.05302i	0.249002	+	0.143761i
$452$	−47.6274	−	39.9641i	−2.24020	−	1.87975i
$453$	−0.689954	−	0.304645i	−0.0324169	−	0.0143135i
$454$	−33.1668	+	5.84820i	−1.55659	+	0.274469i
$455$	11.9380	+	23.6761i	0.559664	+	1.10995i
$456$	7.80638	+	26.9110i	0.365567	+	1.26022i
$457$	−7.74361	−	21.2754i	−0.362231	−	0.995221i	−0.978239	−	0.207481i	$-0.933473\pi$
$457$	−7.74361	−	21.2754i	−0.362231	−	0.995221i	0.616008	−	0.787740i	$-0.288749\pi$
$458$			50.9083i			2.37879i
$459$	1.59288	−	7.84982i	0.0743492	−	0.366398i
$460$	43.0836	+	21.7155i	2.00878	+	1.01249i
$461$	20.2441	−	7.36826i	0.942863	−	0.343174i	0.175567	−	0.984467i	$-0.443824\pi$
$461$	20.2441	−	7.36826i	0.942863	−	0.343174i	0.767296	+	0.641294i	$0.221602\pi$
$462$	7.45979	+	4.36190i	0.347061	+	0.202934i
$463$	21.4013	+	25.5051i	0.994604	+	1.18532i	0.982664	+	0.185395i	$0.0593563\pi$
$463$	21.4013	+	25.5051i	0.994604	+	1.18532i	0.0119402	+	0.999929i	$0.496199\pi$
$464$	33.7096	−	5.94390i	1.56493	−	0.275939i
$465$	5.18015	+	31.1997i	0.240224	+	1.44685i
$466$	−52.0179	−	43.6482i	−2.40968	−	2.02196i
$467$	31.1479	+	17.9832i	1.44135	+	0.832165i	0.997940	−	0.0641526i	$-0.0204344\pi$
$467$	31.1479	+	17.9832i	1.44135	+	0.832165i	0.443412	+	0.896318i	$0.353768\pi$
$468$	59.5563	+	7.99635i	2.75299	+	0.369631i
$469$	24.0742	+	25.3620i	1.11164	+	1.17111i
$470$	1.34888	+	1.00724i	0.0622191	+	0.0464604i
$471$	−28.9409	−	1.93420i	−1.33353	−	0.0891233i
$472$	−49.9944	−	18.1965i	−2.30118	−	0.837561i
$473$	6.55929	+	2.38738i	0.301596	+	0.109772i
$474$	28.9810	+	58.9583i	1.33114	+	2.70804i
$475$	−5.74733	−	11.5269i	−0.263706	−	0.528890i
$476$	−12.5482	−	13.2195i	−0.575148	−	0.605914i
$477$	−19.1729	−	10.0434i	−0.877867	−	0.459857i
$478$	−53.5460	−	30.9148i	−2.44914	−	1.41401i
$479$	−9.02032	−	7.56895i	−0.412149	−	0.345834i	0.413018	−	0.910723i	$-0.364475\pi$
$479$	−9.02032	−	7.56895i	−0.412149	−	0.345834i	−0.825167	+	0.564889i	$0.808919\pi$
$480$	7.25689	−	19.3342i	0.331230	−	0.882482i
$481$	22.5794	−	3.98136i	1.02953	−	0.181534i
$482$	−6.77547	−	8.07469i	−0.308614	−	0.367792i
$483$	−22.1242	−	0.121918i	−1.00669	−	0.00554748i
$484$	−43.8869	+	15.9735i	−1.99486	+	0.726069i
$485$	−5.44223	−	2.74305i	−0.247119	−	0.124556i
$486$	−29.9764	+	25.9501i	−1.35976	+	1.17712i
$487$			30.9740i			1.40357i	0.712390	+	0.701784i	$0.247613\pi$
$487$			30.9740i			1.40357i	−0.712390	+	0.701784i	$0.752387\pi$
$488$	−6.81380	−	18.7208i	−0.308446	−	0.847450i
$489$	−21.6724	−	5.33270i	−0.980060	−	0.241153i
$490$	−30.3779	+	25.7315i	−1.37233	+	1.16243i
$491$	−6.14500	+	1.08353i	−0.277320	+	0.0488990i	−0.310578	−	0.950548i	$-0.600523\pi$
$491$	−6.14500	+	1.08353i	−0.277320	+	0.0488990i	0.0332582	+	0.999447i	$0.489412\pi$
$492$	6.85899	+	63.3807i	0.309227	+	2.85742i
$493$	5.74586	+	4.82135i	0.258781	+	0.217143i
$494$	−25.4316	−	14.6829i	−1.14422	−	0.660617i
$495$	−4.04378	+	2.89542i	−0.181754	+	0.130140i
$496$	49.7486	−	28.7224i	2.23378	−	1.28967i
$497$	0.144762	+	2.36155i	0.00649347	+	0.105930i
$498$	33.3466	−	16.3915i	1.49430	−	0.734523i
$499$	8.95026	+	3.25763i	0.400669	+	0.145831i	0.534492	−	0.845174i	$-0.320503\pi$
$499$	8.95026	+	3.25763i	0.400669	+	0.145831i	−0.133823	+	0.991005i	$0.542725\pi$
$500$	−8.88989	+	49.1688i	−0.397568	+	2.19890i
$501$	1.20449	−	18.0225i	0.0538128	−	0.805186i
$502$	6.84650	−	38.8285i	0.305574	−	1.73300i
$503$	−30.4966	+	17.6072i	−1.35977	+	0.785066i	−0.989593	−	0.143893i	$-0.954038\pi$
$503$	−30.4966	+	17.6072i	−1.35977	+	0.785066i	−0.370181	+	0.928959i	$0.620704\pi$
$504$	5.08979	+	49.5854i	0.226717	+	2.20871i
$505$	−9.74064	+	6.38636i	−0.433453	+	0.284189i
$506$	−5.85206	+	6.97421i	−0.260156	+	0.310042i
$507$	−9.90967	+	7.24653i	−0.440104	+	0.321830i
$508$	−29.6380	+	5.22598i	−1.31497	+	0.231865i
$509$	−5.12539	+	4.30071i	−0.227179	+	0.190626i	−0.749271	−	0.662263i	$-0.769596\pi$
$509$	−5.12539	+	4.30071i	−0.227179	+	0.190626i	0.522092	+	0.852889i	$0.325152\pi$
$510$	14.3202	−	5.05051i	0.634110	−	0.223640i
$511$	20.6021	+	31.1172i	0.911385	+	1.37654i
$512$	50.8452			2.24706
$513$	12.6917	−	4.25380i	0.560350	−	0.187810i
$514$		−	71.8296i		−	3.16827i
$515$	−23.4634	−	2.77688i	−1.03392	−	0.122364i
$516$	20.3035	+	69.9925i	0.893812	+	3.08125i
$517$	−0.168113	+	0.141064i	−0.00739362	+	0.00620398i
$518$	13.7310	+	31.5673i	0.603304	+	1.38699i
$519$	10.2587	−	23.2337i	0.450307	−	1.01985i
$520$	24.8448	+	57.8264i	1.08952	+	2.53586i
$521$	−12.5760	+	21.7822i	−0.550963	+	0.954296i	0.447242	+	0.894413i	$0.352406\pi$
$521$	−12.5760	+	21.7822i	−0.550963	+	0.954296i	−0.998205	+	0.0598833i	$0.980927\pi$
$522$	−7.94293	−	36.2687i	−0.347653	−	1.58744i
$523$	−1.90047	−	3.29171i	−0.0831018	−	0.143937i	0.821479	−	0.570239i	$-0.193149\pi$
$523$	−1.90047	−	3.29171i	−0.0831018	−	0.143937i	−0.904581	+	0.426302i	$0.859816\pi$
$524$	3.71260	−	21.0552i	0.162186	−	0.919801i
$525$	−6.38682	−	22.0047i	−0.278744	−	0.960366i
$526$	16.7425	+	6.09376i	0.730006	+	0.265700i
$527$	11.8287	+	4.30528i	0.515265	+	0.187541i
$528$	7.50463	+	5.02838i	0.326597	+	0.218832i
$529$	0.0537055	−	0.304579i	0.00233502	−	0.0132426i
$530$	−2.32658	−	40.9664i	−0.101060	−	1.77947i
$531$	−7.70478	+	24.2194i	−0.334359	+	1.05103i
$532$	8.64698	−	29.2064i	0.374894	−	1.26626i
$533$	−28.2765	−	23.7268i	−1.22479	−	1.02772i
$534$	−29.9649	−	13.2308i	−1.29671	−	0.572554i
$535$	−9.09380	+	30.2163i	−0.393159	+	1.30636i
$536$	53.3526	+	63.5831i	2.30448	+	2.74637i
$537$	−3.43560	−	11.8436i	−0.148257	−	0.511088i
$538$	56.5689	−	20.5894i	2.43886	−	0.887672i
$539$	−2.35740	−	4.62353i	−0.101540	−	0.199150i
$540$	−49.3227	−	16.2357i	−2.12251	−	0.698674i
$541$	−20.1262			−0.865291			−0.432646	−	0.901564i	$-0.642420\pi$
$541$	−20.1262			−0.865291			−0.432646	+	0.901564i	$0.642420\pi$
$542$	2.74209	+	7.53382i	0.117783	+	0.323605i
$543$	−24.0980	+	25.1085i	−1.03414	+	1.07751i
$544$	−5.28334	−	6.29644i	−0.226521	−	0.269957i
$545$	−3.77211	+	12.5337i	−0.161579	+	0.536886i
$546$	−39.8321	−	33.7989i	−1.70466	−	1.44646i
$547$	11.6827	−	13.9229i	0.499517	−	0.595301i	−0.456095	−	0.889931i	$-0.650752\pi$
$547$	11.6827	−	13.9229i	0.499517	−	0.595301i	0.955611	+	0.294631i	$0.0951966\pi$
$548$	−27.4634	+	47.5679i	−1.17318	+	2.03200i
$549$	−8.80188	+	3.61941i	−0.375655	+	0.154473i
$550$	−8.64665	−	3.75950i	−0.368694	−	0.160306i
$551$	−2.17664	+	12.3443i	−0.0927279	+	0.525886i
$552$	−52.3982	−	3.50192i	−2.23022	−	0.149052i
$553$	4.46113	−	39.2024i	0.189706	−	1.66705i
$554$	2.85851	−	7.85369i	0.121446	−	0.333671i
$555$	−19.8115	−	0.198161i	−0.840953	−	0.00841146i
$556$	6.75452	+	1.19100i	0.286455	+	0.0505098i
$557$	15.4918	+	26.8326i	0.656409	+	1.13693i	0.981539	+	0.191264i	$0.0612587\pi$
$557$	15.4918	+	26.8326i	0.656409	+	1.13693i	−0.325130	+	0.945669i	$0.605408\pi$
$558$	−33.3437	−	52.6369i	−1.41155	−	2.22830i
$559$	−36.5438	−	21.0985i	−1.54564	−	0.892373i
$560$	−33.3424	+	24.9055i	−1.40897	+	1.05245i
$561$	0.212976	+	1.96801i	0.00899185	+	0.0830895i
$562$	74.8203	−	13.1928i	3.15610	−	0.556506i
$563$	−25.4766	−	30.3618i	−1.07371	−	1.27960i	−0.958141	−	0.286298i	$-0.907575\pi$
$563$	−25.4766	−	30.3618i	−1.07371	−	1.27960i	−0.115569	−	0.993299i	$-0.536869\pi$
$564$	−2.22489	−	0.547455i	−0.0936848	−	0.0230520i
$565$	−30.8921	−	3.65606i	−1.29964	−	0.153812i
$566$	13.6857			0.575255
$567$	23.5675	−	3.40185i	0.989742	−	0.142864i
$568$			5.61593i			0.235639i
$569$	−6.04291	−	16.6028i	−0.253332	−	0.696024i	−0.999540	−	0.0303116i	$-0.990350\pi$
$569$	−6.04291	−	16.6028i	−0.253332	−	0.696024i	0.746209	−	0.665712i	$-0.231872\pi$
$570$	19.2750	+	16.5049i	0.807339	+	0.691316i
$571$	9.31684	−	7.81776i	0.389898	−	0.327163i	−0.426676	−	0.904405i	$-0.640315\pi$
$571$	9.31684	−	7.81776i	0.389898	−	0.327163i	0.816573	+	0.577242i	$0.195871\pi$
$572$	−14.6249	+	2.57877i	−0.611498	+	0.107824i
$573$	−12.1981	+	1.32007i	−0.509584	+	0.0551467i
$574$	24.7220	−	49.6017i	1.03188	−	2.07033i
$575$	23.9846	−	2.73311i	1.00023	−	0.113979i
$576$	−0.0624755	−	1.52050i	−0.00260315	−	0.0633540i
$577$	−14.8554	−	25.7303i	−0.618439	−	1.07117i	−0.989771	−	0.142668i	$-0.954432\pi$
$577$	−14.8554	−	25.7303i	−0.618439	−	1.07117i	0.371332	−	0.928500i	$-0.378901\pi$
$578$	−6.45881	+	36.6297i	−0.268651	+	1.52360i
$579$	−1.43428	+	0.705022i	−0.0596068	+	0.0292997i
$580$	35.4173	−	33.3178i	1.47062	−	1.38345i
$581$	−22.1727	−	2.52320i	−0.919880	−	0.104680i
$582$	11.9802	+	0.800669i	0.496595	+	0.0331888i
$583$	5.26777	+	0.928850i	0.218169	+	0.0384690i
$584$	44.2908	+	76.7139i	1.83277	+	3.17444i
$585$	27.1136	−	12.9926i	1.12101	−	0.537179i
$586$	50.9098	+	29.3928i	2.10306	+	1.21421i
$587$	−12.7377	+	15.1802i	−0.525741	+	0.626553i	−0.961928	−	0.273303i	$-0.911884\pi$
$587$	−12.7377	+	15.1802i	−0.525741	+	0.626553i	0.436188	+	0.899856i	$0.356328\pi$
$588$	24.4374	−	48.3613i	1.00778	−	1.99439i
$589$	3.65287	+	20.7165i	0.150514	+	0.853607i
$590$	−46.8991	+	11.0437i	−1.93080	+	0.454661i
$591$	9.12120	+	8.75412i	0.375196	+	0.360096i
$592$	12.3080	+	33.8158i	0.505854	+	1.38982i
$593$		−	4.54610i		−	0.186686i	−0.995634	−	0.0933430i	$-0.970245\pi$
$593$		−	4.54610i		−	0.186686i	0.995634	−	0.0933430i	$-0.0297553\pi$
$594$	5.11541	−	8.35720i	0.209888	−	0.342900i
$595$	−8.87710	−	2.08892i	−0.363925	−	0.0856374i
$596$	−16.4763	−	45.2684i	−0.674897	−	1.85427i
$597$	−4.33140	−	14.9317i	−0.177272	−	0.611113i
$598$	42.1606	−	35.3770i	1.72408	−	1.44667i
$599$	−19.1115	+	3.36988i	−0.780876	+	0.137690i	−0.549856	−	0.835259i	$-0.685317\pi$
$599$	−19.1115	+	3.36988i	−0.780876	+	0.137690i	−0.231020	+	0.972949i	$0.574206\pi$
$600$	−11.9357	−	53.0605i	−0.487274	−	2.16618i
$601$	−1.26699	+	1.50994i	−0.0516817	+	0.0615918i	−0.791266	−	0.611472i	$-0.790578\pi$
$601$	−1.26699	+	1.50994i	−0.0516817	+	0.0615918i	0.739584	+	0.673064i	$0.235022\pi$
$602$	17.9857	−	60.7492i	0.733044	−	2.47595i
$603$	29.3022	−	26.7124i	1.19328	−	1.08781i
$604$	0.973029	+	1.68534i	0.0395920	+	0.0685754i
$605$	−13.9813	+	18.7235i	−0.568419	+	0.761219i
$606$	12.7733	−	19.0636i	0.518882	−	0.774407i
$607$	29.6483	+	10.7911i	1.20339	+	0.437997i	0.864405	−	0.502797i	$-0.167695\pi$
$607$	29.6483	+	10.7911i	1.20339	+	0.437997i	0.338981	+	0.940793i	$0.389918\pi$
$608$	4.69793	−	12.9075i	0.190526	−	0.523467i
$609$	−7.74181	+	20.9112i	−0.313714	+	0.847363i
$610$	−14.4563	−	10.7949i	−0.585320	−	0.437071i
$611$	1.14892	−	0.663331i	0.0464804	−	0.0268355i
$612$	−15.2732	+	13.9234i	−0.617383	+	0.562818i
$613$	−0.790195	−	0.456219i	−0.0319157	−	0.0184265i	0.483957	−	0.875092i	$-0.339199\pi$
$613$	−0.790195	−	0.456219i	−0.0319157	−	0.0184265i	−0.515873	+	0.856665i	$0.672532\pi$
$614$	−40.9674	−	34.3757i	−1.65331	−	1.38729i
$615$	20.2576	+	24.6384i	0.816866	+	0.993517i
$616$	−4.91360	−	11.2963i	−0.197974	−	0.455140i
$617$	11.4019	−	9.56731i	0.459022	−	0.385165i	−0.383749	−	0.923437i	$-0.625367\pi$
$617$	11.4019	−	9.56731i	0.459022	−	0.385165i	0.842771	+	0.538272i	$0.180923\pi$
$618$	44.7059	−	12.9683i	1.79833	−	0.521663i
$619$	1.40271	+	3.85392i	0.0563798	+	0.154902i	0.964685	−	0.263405i	$-0.0848456\pi$
$619$	1.40271	+	3.85392i	0.0563798	+	0.154902i	−0.908305	+	0.418308i	$0.862623\pi$
$620$	36.7295	−	72.8715i	1.47509	−	2.92659i
$621$	−0.643852	+	25.0786i	−0.0258369	+	1.00637i
$622$	50.5543			2.02704
$623$	10.8601	+	16.4030i	0.435103	+	0.657173i
$624$	−39.3994	−	37.8137i	−1.57724	−	1.51376i
$625$	9.76905	+	23.0123i	0.390762	+	0.920492i
$626$	9.75711	+	55.3353i	0.389973	+	2.21164i
$627$	−2.67026	+	1.95265i	−0.106640	+	0.0779812i
$628$	57.3314	+	48.1068i	2.28777	+	1.91967i
$629$	−3.94280	+	6.82912i	−0.157210	+	0.272295i
$630$	28.4766	+	35.0264i	1.13453	+	1.39549i
$631$	−1.46621	−	2.53955i	−0.0583689	−	0.101098i	0.835364	−	0.549696i	$-0.185257\pi$
$631$	−1.46621	−	2.53955i	−0.0583689	−	0.101098i	−0.893733	+	0.448599i	$0.851923\pi$
$632$	16.2625	−	92.2291i	0.646887	−	3.66868i
$633$	5.95702	+	0.398124i	0.236770	+	0.0158240i
$634$	9.40055	+	3.42152i	0.373344	+	0.135886i
$635$	−10.9676	+	10.3175i	−0.435237	+	0.409437i
$636$	24.6362	+	50.1194i	0.976889	+	1.98736i
$637$	9.18095	+	30.0003i	0.363763	+	1.18865i
$638$	4.58784	+	7.94637i	0.181634	+	0.314600i
$639$	2.68051	−	0.110139i	0.106039	−	0.00435704i
$640$	22.3546	−	14.6566i	0.883643	−	0.579353i
$641$	7.35725	−	8.76803i	0.290594	−	0.346316i	−0.600920	−	0.799309i	$-0.705199\pi$
$641$	7.35725	−	8.76803i	0.290594	−	0.346316i	0.891514	+	0.452993i	$0.149644\pi$
$642$	−6.68869	−	61.8070i	−0.263982	−	2.43933i
$643$	1.69315	+	9.60230i	0.0667711	+	0.378678i	0.999821	+	0.0189303i	$0.00602608\pi$
$643$	1.69315	+	9.60230i	0.0667711	+	0.378678i	−0.933050	+	0.359748i	$0.882863\pi$
$644$	45.8940	+	33.9500i	1.80848	+	1.33782i
$645$	27.6970	+	23.7166i	1.09057	+	0.933842i
$646$	9.49078	−	3.45436i	0.373410	−	0.135910i
$647$		−	4.47185i		−	0.175806i	−0.996129	−	0.0879032i	$-0.971983\pi$
$647$		−	4.47185i		−	0.175806i	0.996129	−	0.0879032i	$-0.0280166\pi$
$648$	56.3294	−	4.63686i	2.21283	−	0.182153i
$649$		−	6.28104i		−	0.246552i
$650$	47.5302	+	31.4584i	1.86429	+	1.23390i
$651$	−0.206213	+	37.4208i	−0.00808211	+	1.46664i
$652$	37.0167	+	44.1148i	1.44969	+	1.72767i
$653$	1.09581	+	6.21463i	0.0428823	+	0.243197i	0.998713	−	0.0507207i	$-0.0161518\pi$
$653$	1.09581	+	6.21463i	0.0428823	+	0.243197i	−0.955831	+	0.293918i	$0.905041\pi$
$654$	−2.77447	−	25.6376i	−0.108490	−	1.00251i
$655$	−4.22277	−	9.82853i	−0.164997	−	0.384033i
$656$	28.9678	−	50.1737i	1.13100	−	1.95895i
$657$	35.7473	−	22.6447i	1.39463	−	0.883454i
$658$	1.37132	+	1.44467i	0.0534596	+	0.0563192i
$659$	12.0310	+	2.12138i	0.468659	+	0.0826373i	0.402990	−	0.915204i	$-0.367971\pi$
$659$	12.0310	+	2.12138i	0.468659	+	0.0826373i	0.0656689	+	0.997841i	$0.479082\pi$
$660$	12.8321	+	0.128351i	0.499490	+	0.00499604i
$661$	13.5224	−	37.1526i	0.525962	−	1.44507i	−0.337823	−	0.941210i	$-0.609691\pi$
$661$	13.5224	−	37.1526i	0.525962	−	1.44507i	0.863785	−	0.503860i	$-0.168087\pi$
$662$	−86.6178	−	31.5263i	−3.36650	−	1.22530i
$663$	0.797975	−	11.9399i	0.0309908	−	0.463706i
$664$	−52.1645	−	9.19800i	−2.02437	−	0.356952i
$665$	−4.39426	−	14.5929i	−0.170402	−	0.565887i
$666$	36.1005	−	14.8448i	1.39886	−	0.575226i
$667$	−20.3449	−	11.7462i	−0.787759	−	0.454813i
$668$	−29.9577	+	35.7022i	−1.15910	+	1.38136i
$669$	7.06396	−	5.16558i	0.273109	−	0.199713i
$670$	71.9793	+	21.6626i	2.78080	+	0.836901i
$671$	1.80172	−	1.51182i	0.0695547	−	0.0583633i
$672$	12.3339	−	21.0936i	0.475789	−	0.813703i
$673$	−11.7036	−	32.1553i	−0.451139	−	1.23949i	−0.931923	−	0.362655i	$-0.881870\pi$
$673$	−11.7036	−	32.1553i	−0.451139	−	1.23949i	0.480784	−	0.876839i	$-0.340352\pi$
$674$			1.47843i			0.0569471i
$675$	−25.0919	+	6.73759i	−0.965789	+	0.259330i
$676$	31.6763			1.21832
$677$	−4.02528	−	11.0594i	−0.154704	−	0.425046i	0.837993	−	0.545681i	$-0.183729\pi$
$677$	−4.02528	−	11.0594i	−0.154704	−	0.425046i	−0.992697	+	0.120635i	$0.961507\pi$
$678$	58.8602	−	17.0742i	2.26051	−	0.655732i
$679$	−5.79723	−	4.28850i	−0.222477	−	0.164578i
$680$	−20.7280	−	6.23822i	−0.794881	−	0.239225i
$681$	9.26376	−	20.9804i	0.354988	−	0.803971i
$682$	11.7962	+	9.89816i	0.451699	+	0.379020i
$683$	−0.363116	+	0.628935i	−0.0138942	+	0.0240655i	−0.872889	−	0.487919i	$-0.837756\pi$
$683$	−0.363116	+	0.628935i	−0.0138942	+	0.0240655i	0.858995	+	0.511984i	$0.171089\pi$
$684$	−32.9125	−	10.4703i	−1.25844	−	0.400340i
$685$	1.55827	+	27.4378i	0.0595382	+	1.04835i
$686$	−40.5774	+	23.9243i	−1.54925	+	0.913434i
$687$	−28.8005	−	19.2974i	−1.09881	−	0.736243i
$688$	22.6520	−	62.2360i	0.863601	−	2.37272i
$689$	−30.3859	−	11.0596i	−1.15761	−	0.421336i
$690$	−41.4230	+	23.3663i	−1.57695	+	0.889540i
$691$	27.8464	+	4.91007i	1.05933	+	0.186788i	0.676057	−	0.736849i	$-0.263687\pi$
$691$	27.8464	+	4.91007i	1.05933	+	0.186788i	0.383269	+	0.923637i	$0.374798\pi$
$692$	−56.7525	+	32.7660i	−2.15740	+	1.24558i
$693$	−5.29540	+	2.56682i	−0.201156	+	0.0975056i
$694$	43.8171	−	75.8935i	1.66328	−	2.88088i
$695$	3.15300	−	1.35467i	0.119600	−	0.0513854i
$696$	−21.3785	+	48.4177i	−0.810352	+	1.83527i
$697$	12.5025	−	2.20453i	0.473566	−	0.0835024i
$698$	22.9957	+	27.4052i	0.870398	+	1.03730i
$699$	44.4113	−	12.8829i	1.67979	−	0.487275i
$700$	−20.2119	+	55.5582i	−0.763938	+	2.09990i
$701$			19.1443i			0.723070i	0.932359	+	0.361535i	$0.117747\pi$
$701$			19.1443i			0.723070i	−0.932359	+	0.361535i	$0.882253\pi$
$702$	−39.2269	+	44.3837i	−1.48052	+	1.67515i
$703$	−13.1780			−0.497017
$704$	0.128629	+	0.353404i	0.00484787	+	0.0133194i
$705$	−1.08114	+	0.381300i	−0.0407180	+	0.0143606i
$706$	−54.9940	−	65.5393i	−2.06973	−	2.46661i
$707$	−12.6378	+	5.49712i	−0.475293	+	0.206740i
$708$	52.9345	−	38.7088i	1.98940	−	1.45477i
$709$	30.1595	+	25.3068i	1.13266	+	0.950418i	0.999174	−	0.0406322i	$-0.0129372\pi$
$709$	30.1595	+	25.3068i	1.13266	+	0.950418i	0.133490	+	0.991050i	$0.457382\pi$
$710$	2.78861	+	4.25326i	0.104655	+	0.159622i
$711$	−44.3403	−	5.95337i	−1.66289	−	0.223269i
$712$	23.3473	+	40.4387i	0.874978	+	1.51551i
$713$	−38.8263	−	6.84612i	−1.45406	−	0.256389i
$714$	17.7108	−	3.02236i	0.662810	−	0.113109i
$715$	−5.41198	+	5.09117i	−0.202397	+	0.190399i
$716$	−10.8827	+	29.9000i	−0.406707	+	1.11742i
$717$	37.7868	−	18.5741i	1.41117	−	0.693664i
$718$	−73.6560	−	12.9875i	−2.74882	−	0.484691i
$719$	−8.10030	−	14.0301i	−0.302090	−	0.523235i	0.674519	−	0.738257i	$-0.264351\pi$
$719$	−8.10030	−	14.0301i	−0.302090	−	0.523235i	−0.976609	+	0.215022i	$0.931018\pi$
$720$	27.4724	+	38.3683i	1.02384	+	1.42990i
$721$	−26.8059	−	7.93629i	−0.998303	−	0.295563i
$722$	−24.0898	−	20.2138i	−0.896530	−	0.752278i
$723$	7.13645	−	0.772299i	0.265408	−	0.0287221i
$724$	88.4319	−	15.5929i	3.28655	−	0.579507i
$725$	5.67919	−	23.6573i	0.210920	−	0.878609i
$726$	10.9999	−	44.7041i	0.408243	−	1.65912i
$727$	−26.4929	+	9.64263i	−0.982567	+	0.357625i	−0.782838	−	0.622226i	$-0.786229\pi$
$727$	−26.4929	+	9.64263i	−0.982567	+	0.357625i	−0.199729	+	0.979851i	$0.564006\pi$
$728$	17.3943	+	72.4090i	0.644676	+	2.68366i
$729$	−3.31792	−	26.7954i	−0.122886	−	0.992421i
$730$	71.6364	+	36.1070i	2.65138	+	1.33638i
$731$	13.6377	−	4.96372i	0.504409	−	0.183590i
$732$	23.8448	+	5.86724i	0.881330	+	0.216860i
$733$	−17.1333	+	14.3765i	−0.632832	+	0.531009i	−0.901807	−	0.432138i	$-0.857759\pi$
$733$	−17.1333	+	14.3765i	−0.632832	+	0.531009i	0.268976	+	0.963147i	$0.413315\pi$
$734$	−2.69285	−	15.2719i	−0.0993947	−	0.563696i
$735$	−3.04204	−	26.9397i	−0.112207	−	0.993685i
$736$	19.7206	+	16.5475i	0.726909	+	0.609949i
$737$	−4.89952	+	8.48622i	−0.180476	+	0.312594i
$738$	−55.6666	−	29.1601i	−2.04912	−	1.07340i
$739$	17.1659	+	29.7323i	0.631459	+	1.09372i	0.987254	+	0.159155i	$0.0508768\pi$
$739$	17.1659	+	29.7323i	0.631459	+	1.09372i	−0.355795	+	0.934564i	$0.615790\pi$
$740$	40.9611	+	30.5866i	1.50576	+	1.12438i
$741$	17.9468	−	8.82176i	0.659292	−	0.324076i
$742$	5.48945	−	48.2388i	0.201524	−	1.77090i
$743$	16.1789	+	5.88865i	0.593547	+	0.216033i	0.621289	−	0.783582i	$-0.286609\pi$
$743$	16.1789	+	5.88865i	0.593547	+	0.216033i	−0.0277417	+	0.999615i	$0.508832\pi$
$744$	−5.92314	+	88.6262i	−0.217153	+	3.24919i
$745$	−19.3129	−	14.4214i	−0.707570	−	0.528358i
$746$	27.7721	−	16.0342i	1.01681	−	0.587054i
$747$	−3.36720	+	25.0787i	−0.123200	+	0.917583i
$748$	2.55379	−	4.42329i	0.0933757	−	0.161731i
$749$	−16.6549	+	33.4159i	−0.608556	+	1.22099i
$750$	−35.3869	−	34.2589i	−1.29215	−	1.25096i
$751$	−4.62807	−	26.2471i	−0.168881	−	0.957771i	−0.944972	−	0.327150i	$-0.893912\pi$
$751$	−4.62807	−	26.2471i	−0.168881	−	0.957771i	0.776091	−	0.630620i	$-0.217199\pi$
$752$	1.33845	+	1.59510i	0.0488081	+	0.0581672i
$753$	19.3713	+	18.5917i	0.705930	+	0.677520i
$754$	−18.9715	−	52.1238i	−0.690901	−	1.89824i
$755$	0.869490	+	0.438250i	0.0316440	+	0.0159495i
$756$	−54.2669	−	28.8091i	−1.97367	−	1.04778i
$757$		−	0.611591i		−	0.0222287i	−0.999938	−	0.0111143i	$-0.996462\pi$
$757$		−	0.611591i		−	0.0222287i	0.999938	−	0.0111143i	$-0.00353788\pi$
$758$	5.17589	−	1.88387i	0.187997	−	0.0684252i
$759$	−1.72725	−	5.95437i	−0.0626953	−	0.216130i
$760$	−8.29143	−	35.2111i	−0.300762	−	1.27724i
$761$	4.86072	+	27.5665i	0.176201	+	0.999284i	0.936749	+	0.350003i	$0.113819\pi$
$761$	4.86072	+	27.5665i	0.176201	+	0.999284i	−0.760548	+	0.649282i	$0.775070\pi$
$762$	11.9828	−	27.1384i	0.434090	−	0.983119i
$763$	−6.90845	+	13.8609i	−0.250103	+	0.501800i
$764$	27.4164	+	15.8289i	0.991892	+	0.572669i
$765$	−2.57101	+	10.0159i	−0.0929552	+	0.362125i
$766$	20.6823	−	11.9409i	0.747283	−	0.431444i
$767$	−6.59346	+	37.3934i	−0.238076	+	1.35020i
$768$	−28.3365	+	42.2909i	−1.02250	+	1.52604i
$769$	−6.83039	+	18.7663i	−0.246310	+	0.676731i	0.753504	+	0.657443i	$0.228362\pi$
$769$	−6.83039	+	18.7663i	−0.246310	+	0.676731i	−0.999814	+	0.0192880i	$0.993860\pi$
$770$	−9.33055	−	6.11544i	−0.336250	−	0.220385i
$771$	40.6364	+	27.2279i	1.46349	+	0.980589i
$772$	4.06106	+	0.716075i	0.146161	+	0.0257721i
$773$	13.3411	−	7.70250i	0.479847	−	0.277040i	−0.240506	−	0.970648i	$-0.577313\pi$
$773$	13.3411	−	7.70250i	0.479847	−	0.277040i	0.720353	+	0.693608i	$0.243980\pi$
$774$	−68.4581	−	21.7782i	−2.46068	−	0.782799i
$775$	−4.62278	−	40.5675i	−0.166055	−	1.45723i
$776$	−13.1118	−	11.0021i	−0.470686	−	0.394953i
$777$	−23.0636	−	4.19790i	−0.827401	−	0.150599i
$778$	−12.9453	+	2.28261i	−0.464112	+	0.0818354i
$779$	13.6373	+	16.2522i	0.488605	+	0.582297i
$780$	−76.2597	−	14.2345i	−2.73054	−	0.509678i
$781$	−0.623022	+	0.226762i	−0.0222935	+	0.00811417i
$782$			18.9289i			0.676897i
$783$	23.5293	+	9.25451i	0.840868	+	0.330729i
$784$	−43.8691	+	22.3675i	−1.56675	+	0.798839i
$785$	37.1864	+	4.40098i	1.32724	+	0.157078i
$786$	15.2052	+	14.5933i	0.542352	+	0.520525i
$787$	6.95056	−	5.83221i	0.247761	−	0.207896i	−0.510447	−	0.859909i	$-0.670520\pi$
$787$	6.95056	−	5.83221i	0.247761	−	0.207896i	0.758207	+	0.652014i	$0.226076\pi$
$788$	−5.66447	−	32.1248i	−0.201788	−	1.14440i
$789$	−9.79389	+	7.16186i	−0.348672	+	0.254969i
$790$	−33.4802	−	77.9254i	−1.19117	−	2.77246i
$791$	−35.2929	−	10.4490i	−1.25487	−	0.371523i
$792$	−12.9185	+	5.31219i	−0.459038	+	0.188760i
$793$	−12.3133	+	7.10912i	−0.437260	+	0.252452i
$794$	−12.2464	+	69.4525i	−0.434607	+	2.46478i
$795$	24.0580	+	14.2126i	0.853249	+	0.504069i
$796$	−13.7203	+	37.6962i	−0.486303	+	1.33611i
$797$	−16.8236	+	46.2225i	−0.595923	+	1.63728i	0.163392	+	0.986561i	$0.447756\pi$
$797$	−16.8236	+	46.2225i	−0.595923	+	1.63728i	−0.759315	+	0.650723i	$0.774466\pi$
$798$	19.1728	+	23.1066i	0.678709	+	0.817966i
$799$	−0.0792325	+	0.449350i	−0.00280304	+	0.0158969i
$800$	−10.6305	+	24.4496i	−0.375845	+	0.864424i
$801$	18.8437	−	11.9369i	0.665810	−	0.421768i
$802$	75.9064	+	43.8246i	2.68035	+	1.54750i
$803$	−6.72213	+	8.01112i	−0.237219	+	0.282706i
$804$	−101.714	+	11.0074i	−3.58717	+	0.388200i
$805$	28.5169	+	1.61517i	1.00509	+	0.0569271i
$806$	−59.8365	−	71.3104i	−2.10765	−	2.51180i
$807$	−9.79504	+	39.8076i	−0.344802	+	1.40130i
$808$	−30.7394	+	11.1882i	−1.08141	+	0.393600i
$809$			6.43364i			0.226195i	0.993584	+	0.113097i	$0.0360772\pi$
$809$			6.43364i			0.226195i	−0.993584	+	0.113097i	$0.963923\pi$
$810$	40.3590	−	31.4823i	1.41807	−	1.10618i
$811$			11.0500i			0.388018i	0.981000	+	0.194009i	$0.0621491\pi$
$811$			11.0500i			0.388018i	−0.981000	+	0.194009i	$0.937851\pi$
$812$	47.9730	−	31.7621i	1.68352	−	1.11463i
$813$	−5.30156	−	1.30450i	−0.185934	−	0.0457508i
$814$	−7.38967	+	6.20067i	−0.259008	+	0.217333i
$815$	27.5910	+	8.30371i	0.966472	+	0.290866i
$816$	18.6729	−	2.02076i	0.653683	−	0.0707409i
$817$	18.5791	+	15.5897i	0.649999	+	0.545414i
$818$	71.1323	+	41.0682i	2.48708	+	1.43592i
$819$	34.2200	−	9.72247i	1.19574	−	0.339730i
$820$	−4.66661	−	82.1694i	−0.162965	−	2.86948i
$821$	−0.810284	−	0.142875i	−0.0282791	−	0.00498637i	0.159491	−	0.987199i	$-0.449015\pi$
$821$	−0.810284	−	0.142875i	−0.0282791	−	0.00498637i	−0.187770	+	0.982213i	$0.560126\pi$
$822$	−23.8847	−	48.5906i	−0.833075	−	1.69479i
$823$	8.01468	−	22.0202i	0.279374	−	0.767575i	−0.718060	−	0.695982i	$-0.754970\pi$
$823$	8.01468	−	22.0202i	0.279374	−	0.767575i	0.997434	−	0.0715930i	$-0.0228083\pi$
$824$	−62.3551	−	22.6954i	−2.17224	−	0.790631i
$825$	5.40450	−	3.46662i	0.188160	−	0.120692i
$826$	−56.9027	+	3.48811i	−1.97990	+	0.121367i
$827$	−10.8253	−	18.7500i	−0.376433	−	0.652001i	0.614108	−	0.789222i	$-0.289516\pi$
$827$	−10.8253	−	18.7500i	−0.376433	−	0.652001i	−0.990540	+	0.137222i	$0.956183\pi$
$828$	39.5368	−	51.2524i	1.37400	−	1.78114i
$829$	−11.7660	−	6.79310i	−0.408650	−	0.235934i	0.281560	−	0.959544i	$-0.409148\pi$
$829$	−11.7660	−	6.79310i	−0.408650	−	0.235934i	−0.690209	+	0.723610i	$0.742482\pi$
$830$	−44.0744	+	18.9363i	−1.52984	+	0.657288i
$831$	3.35955	+	4.59420i	0.116541	+	0.159371i
$832$	−0.394791	−	2.23897i	−0.0136869	−	0.0776224i
$833$	−9.93378	−	4.21344i	−0.344185	−	0.145987i
$834$	−4.68153	+	4.87784i	−0.162108	+	0.168906i
$835$	−2.74064	+	23.1572i	−0.0948438	+	0.801389i
$836$	8.53550			0.295206
$837$	42.4179	+	1.08901i	1.46618	+	0.0376417i
$838$	−55.0217			−1.90069
$839$	−0.166559	+	0.0606223i	−0.00575024	+	0.00209292i	−0.344894	−	0.938642i	$-0.612085\pi$
$839$	−0.166559	+	0.0606223i	−0.00575024	+	0.00209292i	0.339143	+	0.940735i	$0.389863\pi$
$840$	−3.29467	−	64.2664i	−0.113677	−	2.21740i
$841$	4.07782	−	3.42169i	0.140614	−	0.117989i
$842$	13.3291	+	75.5928i	0.459350	+	2.60510i
$843$	−20.8979	+	47.3293i	−0.719763	+	1.63011i
$844$	−11.8007	−	9.90200i	−0.406199	−	0.340841i
$845$	13.2542	−	8.68999i	0.455958	−	0.298945i
$846$	1.66911	−	1.52160i	0.0573853	−	0.0523136i
$847$	−20.0532	+	19.0350i	−0.689037	+	0.654051i
$848$	8.81313	−	49.9818i	0.302644	−	1.71638i
$849$	−5.18776	+	7.74249i	−0.178043	+	0.265722i
$850$	−18.7960	+	5.56799i	−0.644699	+	0.190980i
$851$	8.44715	−	23.2084i	0.289565	−	0.795573i
$852$	−5.75064	−	3.85314i	−0.197014	−	0.132006i
$853$	3.32391	−	18.8508i	0.113809	−	0.645440i	−0.873525	−	0.486780i	$-0.838171\pi$
$853$	3.32391	−	18.8508i	0.113809	−	0.645440i	0.987333	−	0.158661i	$-0.0507175\pi$
$854$	−14.6968	−	15.4830i	−0.502916	−	0.529818i
$855$	−16.6438	+	4.64810i	−0.569207	+	0.158962i
$856$	−44.3112	+	76.7492i	−1.51452	+	2.62323i
$857$	17.1808	−	20.4753i	0.586885	−	0.699423i	−0.388119	−	0.921609i	$-0.626875\pi$
$857$	17.1808	−	20.4753i	0.586885	−	0.699423i	0.975004	+	0.222187i	$0.0713195\pi$
$858$	5.91291	−	13.3914i	0.201863	−	0.457177i
$859$	−34.6107	+	6.10280i	−1.18090	+	0.208225i	−0.729426	−	0.684059i	$-0.760213\pi$
$859$	−34.6107	+	6.10280i	−1.18090	+	0.208225i	−0.451475	+	0.892284i	$0.649102\pi$
$860$	−21.5651	−	91.5801i	−0.735363	−	3.12286i
$861$	18.6902	+	32.7883i	0.636959	+	1.11742i
$862$	−19.7241	−	54.1915i	−0.671805	−	1.84577i
$863$	−29.6880			−1.01059			−0.505296	−	0.862946i	$-0.668617\pi$
$863$	−29.6880			−1.01059			−0.505296	+	0.862946i	$0.668617\pi$
$864$	−23.6311	−	14.4645i	−0.803948	−	0.492094i
$865$	−14.7577	+	29.2794i	−0.501778	+	0.995530i
$866$	−38.3745	+	13.9672i	−1.30402	+	0.474624i
$867$	−18.2744	−	17.5389i	−0.620631	−	0.595654i
$868$	57.4230	−	77.6249i	1.94906	−	2.63476i
$869$	10.8884	−	1.91992i	0.369364	−	0.0651288i
$870$	7.85082	+	47.2850i	0.266168	+	1.60311i
$871$	38.0770	−	45.3784i	1.29019	−	1.53759i
$872$	−18.3803	+	31.8356i	−0.622435	+	1.07809i
$873$	−4.99421	+	6.47409i	−0.169028	+	0.219115i
$874$	−27.3950	+	15.8165i	−0.926649	+	0.535001i
$875$	6.78449	+	28.7919i	0.229358	+	0.973342i
$876$	−108.942	−	7.28092i	−3.68082	−	0.245999i
$877$	−7.95670	+	21.8609i	−0.268679	+	0.738189i	0.729832	+	0.683627i	$0.239598\pi$
$877$	−7.95670	+	21.8609i	−0.268679	+	0.738189i	−0.998510	+	0.0545619i	$0.982624\pi$
$878$	3.85603	−	10.5944i	0.130135	−	0.357542i
$879$	−35.9265	+	17.6597i	−1.21177	+	0.595647i
$880$	−9.34444	−	6.97770i	−0.315001	−	0.235218i
$881$	−21.4076	−	37.0791i	−0.721241	−	1.24923i	−0.960502	−	0.278272i	$-0.910238\pi$
$881$	−21.4076	−	37.0791i	−0.721241	−	1.24923i	0.239261	−	0.970955i	$-0.423095\pi$
$882$	26.1947	+	46.5479i	0.882022	+	1.56735i
$883$	46.5253	+	26.8614i	1.56570	+	0.903959i	0.996661	+	0.0816501i	$0.0260190\pi$
$883$	46.5253	+	26.8614i	1.56570	+	0.903959i	0.569042	+	0.822309i	$0.307314\pi$
$884$	−19.8470	+	23.6527i	−0.667525	+	0.795526i
$885$	11.5299	−	30.7186i	0.387574	−	1.03260i
$886$	2.37761	+	13.4841i	0.0798775	+	0.453008i
$887$	−15.6254	−	18.6216i	−0.524648	−	0.625251i	0.437025	−	0.899449i	$-0.356032\pi$
$887$	−15.6254	−	18.6216i	−0.524648	−	0.625251i	−0.961673	+	0.274198i	$0.911588\pi$
$888$	−54.0318	−	13.2950i	−1.81319	−	0.446152i
$889$	−14.8557	+	9.83572i	−0.498246	+	0.329879i
$890$	37.7622	+	19.0333i	1.26579	+	0.637998i
$891$	2.78889	+	6.06187i	0.0934313	+	0.203080i
$892$	−22.5800			−0.756035
$893$	−0.716528	+	0.260795i	−0.0239777	+	0.00872717i
$894$	46.1113	+	11.3461i	1.54219	+	0.379471i
$895$	3.64907	+	15.4965i	0.121975	+	0.517990i
$896$	29.0035	−	12.6158i	0.968939	−	0.421464i
$897$	4.03243	+	37.2618i	0.134639	+	1.24413i
$898$	−28.8490	+	34.3809i	−0.962704	+	1.14731i
$899$	−19.8674	+	34.4114i	−0.662615	+	1.14768i
$900$	62.5224	+	24.1832i	2.08408	+	0.806108i
$901$	9.63143	−	5.56071i	0.320869	−	0.185254i
$902$	15.2944	+	2.69682i	0.509249	+	0.0897943i
$903$	27.5502	+	33.2029i	0.916813	+	1.10492i
$904$	−82.0972	−	29.8809i	−2.73051	−	0.993825i
$905$	32.7244	−	30.7846i	1.08780	−	1.02331i
$906$	−1.91404	−	0.127921i	−0.0635897	−	0.00424988i
$907$	−14.9941	−	2.64387i	−0.497873	−	0.0877884i	−0.0809274	−	0.996720i	$-0.525788\pi$
$907$	−14.9941	−	2.64387i	−0.497873	−	0.0877884i	−0.416945	+	0.908932i	$0.636899\pi$
$908$	−51.2484	+	29.5883i	−1.70074	+	0.981921i
$909$	5.94305	+	14.4526i	0.197119	+	0.479363i
$910$	49.1286	+	46.2022i	1.62860	+	1.53159i
$911$	14.3312	−	17.0793i	0.474814	−	0.565862i	−0.474474	−	0.880270i	$-0.657362\pi$
$911$	14.3312	−	17.0793i	0.474814	−	0.565862i	0.949288	+	0.314408i	$0.101806\pi$
$912$	18.5272	+	25.3360i	0.613495	+	0.838958i
$913$	−1.08590	−	6.15844i	−0.0359380	−	0.203815i
$914$	−37.0153	−	44.1131i	−1.22436	−	1.45913i
$915$	11.5869	−	4.08651i	0.383050	−	0.135096i
$916$	30.5941	+	84.0566i	1.01086	+	2.77731i
$917$	−2.95644	−	12.3071i	−0.0976303	−	0.406415i
$918$	−3.02156	−	20.1471i	−0.0997264	−	0.664955i
$919$	13.0256			0.429677			0.214838	−	0.976650i	$-0.431078\pi$
$919$	13.0256			0.429677			0.214838	+	0.976650i	$0.431078\pi$
$920$	67.3269	+	7.96809i	2.21970	+	0.262700i
$921$	34.9767	−	10.1461i	1.15252	−	0.334325i
$922$	41.9748	−	35.2211i	1.38237	−	1.15994i
$923$	3.94713	−	0.695985i	0.129921	−	0.0229086i
$924$	14.9385	+	2.71902i	0.491441	+	0.0894493i
$925$	25.5302	+	1.56106i	0.839427	+	0.0513274i
$926$	73.3374	+	42.3414i	2.41002	+	1.39142i
$927$	−9.60971	+	30.2075i	−0.315624	+	0.992143i
$928$	22.4695	−	12.9728i	0.737597	−	0.425852i
$929$	7.34332	−	41.6461i	0.240927	−	1.36636i	−0.588839	−	0.808251i	$-0.700415\pi$
$929$	7.34332	−	41.6461i	0.240927	−	1.36636i	0.829765	−	0.558112i	$-0.188474\pi$
$930$	39.5217	+	70.0627i	1.29597	+	2.29745i
$931$	−2.20248	−	17.8973i	−0.0721832	−	0.586562i
$932$	−112.120	−	40.8083i	−3.67261	−	1.33672i
$933$	−19.1633	+	28.6003i	−0.627377	+	0.936331i
$934$	90.0889	+	15.8851i	2.94780	+	0.519776i
$935$	−0.144901	−	2.55141i	−0.00473878	−	0.0834401i
$936$	82.4849	−	18.0644i	2.69610	−	0.590454i
$937$	−10.2841	+	17.8126i	−0.335967	+	0.581913i	−0.983670	−	0.179981i	$-0.942397\pi$
$937$	−10.2841	+	17.8126i	−0.335967	+	0.581913i	0.647703	+	0.761893i	$0.275730\pi$
$938$	79.6013	+	39.6742i	2.59907	+	1.29541i
$939$	−35.0036	−	15.4556i	−1.14230	−	0.504375i
$940$	2.83250	+	0.852460i	0.0923859	+	0.0278042i
$941$	3.07590	−	2.58099i	0.100271	−	0.0841378i	−0.591274	−	0.806471i	$-0.701375\pi$
$941$	3.07590	−	2.58099i	0.100271	−	0.0841378i	0.691545	+	0.722333i	$0.256930\pi$
$942$	−70.8529	+	20.5531i	−2.30851	+	0.669656i
$943$	−37.3642	+	13.5994i	−1.21674	+	0.442859i
$944$	−59.5959			−1.93968
$945$	−30.6100	+	2.83295i	−0.995745	+	0.0921559i
$946$	17.7538			0.577227
$947$	9.57429	−	3.48476i	0.311123	−	0.113239i	−0.181740	−	0.983347i	$-0.558173\pi$
$947$	9.57429	−	3.48476i	0.311123	−	0.113239i	0.492862	+	0.870107i	$0.335951\pi$
$948$	83.2835	+	79.9318i	2.70492	+	2.59606i
$949$	48.4289	−	40.6367i	1.57207	−	1.31912i
$950$	−23.7638	−	22.5502i	−0.770998	−	0.731625i
$951$	−5.49907	+	4.02124i	−0.178320	+	0.130398i
$952$	−22.9229	−	11.4250i	−0.742935	−	0.370287i
$953$	−13.5411	+	23.4539i	−0.438639	+	0.759745i	−0.997585	−	0.0694593i	$-0.977873\pi$
$953$	−13.5411	+	23.4539i	−0.438639	+	0.759745i	0.558946	+	0.829204i	$0.311206\pi$
$954$	−54.5611	−	7.32567i	−1.76648	−	0.237177i
$955$	15.8142	−	0.898128i	0.511735	−	0.0290627i
$956$	−106.991	−	18.8653i	−3.46032	−	0.610148i
$957$	−6.23461	−	0.416677i	−0.201536	−	0.0134692i
$958$	−28.1433	−	10.2433i	−0.909270	−	0.330947i
$959$	−3.67664	+	32.3087i	−0.118725	+	1.04330i
$960$	−0.0196496	+	1.96451i	−0.000634189	+	0.0634043i
$961$	−6.19642	+	35.1416i	−0.199884	+	1.13360i
$962$	50.5026	−	29.1577i	1.62827	−	0.940081i
$963$	37.5018	+	19.6447i	1.20848	+	0.633043i
$964$	−16.0398	−	9.26061i	−0.516609	−	0.298264i
$965$	1.89570	−	0.814475i	0.0610247	−	0.0262189i
$966$	−52.9841	+	18.9546i	−1.70473	+	0.609855i
$967$	6.31273	−	1.11310i	0.203004	−	0.0357950i	−0.0712216	−	0.997461i	$-0.522690\pi$
$967$	6.31273	−	1.11310i	0.203004	−	0.0357950i	0.274225	+	0.961666i	$0.411579\pi$
$968$	−50.2739	+	42.1848i	−1.61587	+	1.35587i
$969$	−1.64335	+	6.67868i	−0.0527920	+	0.214550i
$970$	−15.3934	−	1.82180i	−0.494253	−	0.0584945i
$971$	−5.57738			−0.178987			−0.0894933	−	0.995987i	$-0.528525\pi$
$971$	−5.57738			−0.178987			−0.0894933	+	0.995987i	$0.528525\pi$
$972$	−33.9000	+	60.8620i	−1.08734	+	1.95215i
$973$	3.94811	−	0.948428i	0.126571	−	0.0304052i
$974$	26.9446	+	74.0296i	0.863359	+	2.37206i
$975$	−35.8141	+	14.9648i	−1.14697	+	0.479256i
$976$	−14.3445	−	17.0951i	−0.459157	−	0.547202i
$977$	0.534760	+	3.03277i	0.0171085	+	0.0970270i	0.992166	−	0.124924i	$-0.0398687\pi$
$977$	0.534760	+	3.03277i	0.0171085	+	0.0970270i	−0.975058	+	0.221951i	$0.928758\pi$
$978$	−56.4371	+	6.10756i	−1.80466	+	0.195298i
$979$	−3.54348	+	4.22296i	−0.113250	+	0.134966i
$980$	−34.6944	+	60.7423i	−1.10827	+	1.94034i
$981$	15.5558	+	8.14864i	0.496657	+	0.260166i
$982$	−13.7443	+	7.93528i	−0.438599	+	0.253225i
$983$	52.7374	+	9.29902i	1.68206	+	0.296593i	0.931374	−	0.364065i	$-0.118611\pi$
$983$	52.7374	+	9.29902i	1.68206	+	0.296593i	0.750687	+	0.660658i	$0.229722\pi$
$984$	39.5183	+	80.3952i	1.25980	+	2.56291i
$985$	−11.1832	−	11.8879i	−0.356326	−	0.378779i
$986$	17.9271	+	6.52491i	0.570914	+	0.207796i
$987$	−1.33712	+	0.228180i	−0.0425609	+	0.00726304i
$988$	−50.8150	−	8.96006i	−1.61664	−	0.285058i
$989$	−39.3650	+	22.7274i	−1.25174	+	0.722690i
$990$	−7.14610	+	10.4379i	−0.227118	+	0.331739i
$991$	−14.0005	+	24.2495i	−0.444739	+	0.770311i	−0.998034	−	0.0626744i	$-0.980037\pi$
$991$	−14.0005	+	24.2495i	−0.444739	+	0.770311i	0.553295	+	0.832986i	$0.313370\pi$
$992$	27.9884	−	33.3553i	0.888633	−	1.05903i
$993$	50.6691	−	37.0522i	1.60793	−	1.17582i
$994$	2.40032	+	5.51830i	0.0761336	+	0.175030i
$995$	4.60053	+	19.5370i	0.145847	+	0.619366i
$996$	45.2091	−	47.1049i	1.43251	−	1.49258i
$997$	22.4100	−	8.15656i	0.709731	−	0.258321i	0.0381711	−	0.999271i	$-0.487847\pi$
$997$	22.4100	−	8.15656i	0.709731	−	0.258321i	0.671560	+	0.740950i	$0.265625\pi$
$998$	24.2254			0.766842
$999$	−5.28612	+	26.0504i	−0.167245	+	0.824198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.209.129	yes	816
5.4	even	2	inner	945.2.cs.b.209.8	yes	816
7.6	odd	2	inner	945.2.cs.b.209.130	yes	816
27.23	odd	18	inner	945.2.cs.b.104.7	✓	816
35.34	odd	2	inner	945.2.cs.b.209.7	yes	816
135.104	odd	18	inner	945.2.cs.b.104.130	yes	816
189.104	even	18	inner	945.2.cs.b.104.8	yes	816
945.104	even	18	inner	945.2.cs.b.104.129	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.7	✓	816	27.23	odd	18	inner
945.2.cs.b.104.8	yes	816	189.104	even	18	inner
945.2.cs.b.104.129	yes	816	945.104	even	18	inner
945.2.cs.b.104.130	yes	816	135.104	odd	18	inner
945.2.cs.b.209.7	yes	816	35.34	odd	2	inner
945.2.cs.b.209.8	yes	816	5.4	even	2	inner
945.2.cs.b.209.129	yes	816	1.1	even	1	trivial
945.2.cs.b.209.130	yes	816	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.39005 - 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(0.644408 - 2.14120i) q^{5} +(0.473977 + 4.37980i) q^{6} +(1.18021 - 2.36793i) q^{7} +(3.14000 - 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +O(q^{10})\)	\(q+(2.39005 - 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(0.644408 - 2.14120i) q^{5} +(0.473977 + 4.37980i) q^{6} +(1.18021 - 2.36793i) q^{7} +(3.14000 - 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +(-0.322477 - 5.67816i) q^{10} +(0.730141 + 0.128744i) q^{11} +(3.41471 + 6.94681i) q^{12} +(-4.21165 - 1.53292i) q^{13} +(0.760868 - 6.68616i) q^{14} +(3.33457 + 1.96994i) q^{15} +(1.22155 - 6.92774i) q^{16} +(1.33497 - 0.770744i) q^{17} +(-7.56246 - 1.01538i) q^{18} +(2.23093 + 1.28803i) q^{19} +(-3.94483 - 9.18163i) q^{20} +(3.49417 + 2.96492i) q^{21} +(1.85707 - 0.327452i) q^{22} +(-3.69844 + 3.10336i) q^{23} +(7.84769 + 7.53185i) q^{24} +(-4.16948 - 2.75961i) q^{25} -11.3996 q^{26} +(3.44108 - 3.89345i) q^{27} +(-2.76185 - 11.4970i) q^{28} +(1.66423 + 4.57243i) q^{29} +(9.68346 + 1.80750i) q^{30} +(5.24901 + 6.25553i) q^{31} +(-0.925915 - 5.25112i) q^{32} +(-0.518696 + 1.17473i) q^{33} +(2.52017 - 3.00342i) q^{34} +(-4.30969 - 4.05297i) q^{35} +(-13.0969 + 2.86825i) q^{36} +(-4.43022 + 2.55779i) q^{37} +(6.45249 + 1.13775i) q^{38} +(4.32115 - 6.44913i) q^{39} +(-9.62177 - 10.2281i) q^{40} +(7.73911 + 2.81680i) q^{41} +(10.9305 + 4.04671i) q^{42} +(9.27186 + 1.63488i) q^{43} +(2.86949 - 1.65670i) q^{44} +(-4.69320 + 4.79311i) q^{45} +(-6.13983 + 10.6345i) q^{46} +(-0.190266 + 0.226750i) q^{47} +(11.1461 + 4.92150i) q^{48} +(-4.21423 - 5.58930i) q^{49} +(-12.3659 - 2.96857i) q^{50} +(0.743834 + 2.56423i) q^{51} +(-18.8223 + 6.85075i) q^{52} +7.21473 q^{53} +(4.83742 - 12.2990i) q^{54} +(0.746175 - 1.48041i) q^{55} +(-9.17249 - 13.8540i) q^{56} +(-3.08956 + 3.21912i) q^{57} +(7.95519 + 9.48063i) q^{58} +(-1.47111 - 8.34311i) q^{59} +(17.0750 - 2.83499i) q^{60} +(2.03914 - 2.43015i) q^{61} +(17.9872 + 10.3849i) q^{62} +(-6.43270 + 4.64978i) q^{63} +(0.253630 + 0.439300i) q^{64} +(-5.99631 + 8.03017i) q^{65} +(-0.217801 + 3.25889i) q^{66} +(-4.52044 + 12.4198i) q^{67} +(2.35619 - 6.47359i) q^{68} +(-3.68891 - 7.50465i) q^{69} +(-13.8261 - 5.93779i) q^{70} +(-0.774450 + 0.447129i) q^{71} +(-15.9154 + 10.0819i) q^{72} +(-7.05268 + 12.2156i) q^{73} +(-8.36341 + 9.96713i) q^{74} +(6.36686 - 5.87053i) q^{75} +(11.3377 - 1.99914i) q^{76} +(1.16657 - 1.57698i) q^{77} +(4.71764 - 19.1728i) q^{78} +(14.0134 - 5.10046i) q^{79} +(-14.0465 - 7.07987i) q^{80} +(5.12426 + 7.39878i) q^{81} +20.9472 q^{82} +(-2.88480 - 7.92592i) q^{83} +(20.4796 + 0.112856i) q^{84} +(-0.790052 - 3.35511i) q^{85} +(23.5824 - 4.15822i) q^{86} +(-8.37903 + 0.906769i) q^{87} +(2.99283 - 3.56672i) q^{88} +(-3.71773 + 6.43929i) q^{89} +(-7.04744 + 15.5384i) q^{90} +(-8.60046 + 8.16377i) q^{91} +(-3.74674 + 21.2488i) q^{92} +(-12.6933 + 6.23942i) q^{93} +(-0.257494 + 0.707458i) q^{94} +(4.19555 - 3.94684i) q^{95} +(9.21497 + 0.615862i) q^{96} +(0.473281 - 2.68411i) q^{97} +(-14.9344 - 9.69273i) q^{98} +(-1.76110 - 1.35854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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