LMFDB - Embedded newform 945.2.cs.b.209.7

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			209.7
Character	$\chi$	$=$	945.209
Dual form			945.2.cs.b.104.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39005 + 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(1.33788 + 1.79167i) q^{5} +(-0.473977 - 4.37980i) q^{6} +(-2.12702 + 1.57346i) q^{7} +(-3.14000 + 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +O(q^{10})$	\(q+(-2.39005 + 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(1.33788 + 1.79167i) q^{5} +(-0.473977 - 4.37980i) q^{6} +(-2.12702 + 1.57346i) q^{7} +(-3.14000 + 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +(-4.75619 - 3.11835i) q^{10} +(0.730141 + 0.128744i) q^{11} +(3.41471 + 6.94681i) q^{12} +(-4.21165 - 1.53292i) q^{13} +(3.71492 - 5.61097i) q^{14} +(-3.56705 + 1.50869i) 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} +(9.72715 + 2.29053i) q^{20} +(-1.76613 - 4.22857i) q^{21} +(-1.85707 + 0.327452i) q^{22} +(3.69844 - 3.10336i) q^{23} +(-7.84769 - 7.53185i) q^{24} +(-1.42016 + 4.79407i) q^{25} +11.3996 q^{26} +(3.44108 - 3.89345i) q^{27} +(-2.76185 + 11.4970i) q^{28} +(1.66423 + 4.57243i) q^{29} +(7.21302 - 6.70885i) 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} +(-5.66482 - 1.70581i) 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} +(-13.9452 + 1.65040i) q^{40} +(-7.73911 - 2.81680i) q^{41} +(7.89961 + 8.57013i) q^{42} +(-9.27186 - 1.63488i) q^{43} +(2.86949 - 1.65670i) q^{44} +(-1.06124 - 6.62373i) q^{45} +(-6.13983 + 10.6345i) q^{46} +(-0.190266 + 0.226750i) q^{47} +(11.1461 + 4.92150i) q^{48} +(2.04843 - 6.69357i) q^{49} +(-0.776154 - 12.6935i) 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} +(-1.87865 - 16.5088i) q^{56} +(3.08956 - 3.21912i) q^{57} +(-7.95519 - 9.48063i) q^{58} +(1.47111 + 8.34311i) q^{59} +(-7.87792 + 15.4120i) q^{60} +(-2.03914 + 2.43015i) q^{61} +(17.9872 + 10.3849i) q^{62} +(7.84286 - 1.22046i) q^{63} +(0.253630 + 0.439300i) q^{64} +(-2.88821 - 9.59675i) 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} +(15.0231 - 0.850892i) 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} +(-7.47535 - 4.37254i) q^{75} +(-11.3377 + 1.99914i) q^{76} +(-1.75560 + 0.875009i) 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} +(-18.1937 - 9.40309i) q^{84} +(3.16694 + 1.36066i) 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} +(8.29845 + 14.9079i) q^{90} +(11.3703 - 3.36634i) q^{91} +(3.74674 - 21.2488i) q^{92} +(12.6933 - 6.23942i) q^{93} +(0.257494 - 0.707458i) q^{94} +(-0.676994 - 5.72030i) q^{95} +(-9.21497 - 0.615862i) q^{96} +(0.473281 - 2.68411i) q^{97} +(0.926942 + 17.7799i) 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	−0.994628	−	0.103510i	$-0.966992\pi$
$2$	−2.39005	+	0.869908i	−1.69002	+	0.615118i	−0.695394	+	0.718628i	$0.744770\pi$
$3$	−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
$5$	1.33788	+	1.79167i	0.598318	+	0.801259i
$5$	1.33788	+	1.79167i	0.598318	+	0.801259i
$6$	−0.473977	−	4.37980i	−0.193500	−	1.78804i
$7$	−2.12702	+	1.57346i	−0.803938	+	0.594713i
$7$	−2.12702	+	1.57346i	−0.803938	+	0.594713i
$8$	−3.14000	+	5.43864i	−1.11016	+	1.92285i
$9$	−2.65747	−	1.39207i	−0.885822	−	0.464024i
$10$	−4.75619	−	3.11835i	−1.50404	−	0.986110i
$11$	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	$0.824602\pi$
$14$	3.71492	−	5.61097i	0.992855	−	1.49960i
$15$	−3.56705	+	1.50869i	−0.921009	+	0.389541i
$16$	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	0.221768	−	0.975100i	$-0.428817\pi$
$19$	−2.23093	−	1.28803i	−0.511809	−	0.295493i	−0.733577	+	0.679606i	$0.762151\pi$
$20$	9.72715	+	2.29053i	2.17506	+	0.512177i
$21$	−1.76613	−	4.22857i	−0.385401	−	0.922749i
$22$	−1.85707	+	0.327452i	−0.395929	+	0.0698129i
$23$	3.69844	−	3.10336i	0.771178	−	0.647095i	−0.169833	−	0.985473i	$-0.554323\pi$
$23$	3.69844	−	3.10336i	0.771178	−	0.647095i	0.941010	+	0.338378i	$0.109878\pi$
$24$	−7.84769	−	7.53185i	−1.60190	−	1.53743i
$25$	−1.42016	+	4.79407i	−0.284031	+	0.958815i
$26$	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	$0.739676\pi$
$30$	7.21302	−	6.70885i	1.31691	−	1.22486i
$31$	−5.24901	−	6.25553i	−0.942750	−	1.12353i	−0.992188	−	0.124749i	$-0.960187\pi$
$31$	−5.24901	−	6.25553i	−0.942750	−	1.12353i	0.0494381	−	0.998777i	$-0.484257\pi$
$32$	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
$35$	−5.66482	−	1.70581i	−0.957530	−	0.288335i
$36$	−13.0969	+	2.86825i	−2.18281	+	0.478042i
$37$	4.43022	−	2.55779i	0.728323	−	0.420498i	−0.0894853	−	0.995988i	$-0.528522\pi$
$37$	4.43022	−	2.55779i	0.728323	−	0.420498i	0.817808	+	0.575491i	$0.195189\pi$
$38$	6.45249	+	1.13775i	1.04673	+	0.184567i
$39$	4.32115	−	6.44913i	0.691938	−	1.03269i
$40$	−13.9452	+	1.65040i	−2.20493	+	0.260951i
$41$	−7.73911	−	2.81680i	−1.20865	−	0.439911i	−0.342412	−	0.939550i	$-0.611244\pi$
$41$	−7.73911	−	2.81680i	−1.20865	−	0.439911i	−0.866234	+	0.499639i	$0.833466\pi$
$42$	7.89961	+	8.57013i	1.21894	+	1.32240i
$43$	−9.27186	−	1.63488i	−1.41395	−	0.249317i	−0.586085	−	0.810250i	$-0.699331\pi$
$43$	−9.27186	−	1.63488i	−1.41395	−	0.249317i	−0.827861	+	0.560933i	$0.810443\pi$
$44$	2.86949	−	1.65670i	0.432592	−	0.249757i
$45$	−1.06124	−	6.62373i	−0.158200	−	0.987407i
$46$	−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
$49$	2.04843	−	6.69357i	0.292633	−	0.956225i
$50$	−0.776154	−	12.6935i	−0.109765	−	1.79513i
$51$	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	$-0.665019\pi$
$53$	−7.21473			−0.991019			−0.495510	+	0.868602i	$0.665019\pi$
$54$	−4.83742	+	12.2990i	−0.658290	+	1.67368i
$55$	0.746175	+	1.48041i	0.100614	+	0.199619i
$56$	−1.87865	−	16.5088i	−0.251046	−	2.20608i
$57$	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	$0.130377\pi$
$59$	1.47111	+	8.34311i	0.191523	+	1.08618i	−0.725761	+	0.687947i	$0.758512\pi$
$60$	−7.87792	+	15.4120i	−1.01703	+	1.98968i
$61$	−2.03914	+	2.43015i	−0.261085	+	0.311148i	−0.880623	−	0.473818i	$-0.842875\pi$
$61$	−2.03914	+	2.43015i	−0.261085	+	0.311148i	0.619538	+	0.784967i	$0.287320\pi$
$62$	17.9872	+	10.3849i	2.28437	+	1.31888i
$63$	7.84286	−	1.22046i	0.988108	−	0.153763i
$64$	0.253630	+	0.439300i	0.0317037	+	0.0549125i
$65$	−2.88821	−	9.59675i	−0.358238	−	1.19033i
$66$	0.217801	−	3.25889i	0.0268094	−	0.401142i
$67$	4.52044	−	12.4198i	0.552259	−	1.51732i	−0.278359	−	0.960477i	$-0.589791\pi$
$67$	4.52044	−	12.4198i	0.552259	−	1.51732i	0.830618	−	0.556842i	$-0.187987\pi$
$68$	2.35619	−	6.47359i	0.285731	−	0.785038i
$69$	3.68891	+	7.50465i	0.444093	+	0.903453i
$70$	15.0231	−	0.850892i	1.79561	−	0.101701i
$71$	−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
$75$	−7.47535	−	4.37254i	−0.863180	−	0.504897i
$76$	−11.3377	+	1.99914i	−1.30052	+	0.229318i
$77$	−1.75560	+	0.875009i	−0.200069	+	0.0997166i
$78$	−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	$-0.264305\pi$
$84$	−18.1937	−	9.40309i	−1.98510	−	1.02596i
$85$	3.16694	+	1.36066i	0.343503	+	0.147584i
$86$	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	−0.598905	−	0.800820i	$-0.704397\pi$
$89$	3.71773	−	6.43929i	0.394078	−	0.682564i	0.992983	+	0.118257i	$0.0377305\pi$
$90$	8.29845	+	14.9079i	0.874733	+	1.57143i
$91$	11.3703	−	3.36634i	1.19193	−	0.352888i
$92$	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
$95$	−0.676994	−	5.72030i	−0.0694581	−	0.586891i
$96$	−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	$0.0113702\pi$
$98$	0.926942	+	17.7799i	0.0936353	+	1.79605i
$99$	−1.76110	−	1.35854i	−0.176998	−	0.136539i
$100$	8.90989	+	20.4923i	0.890989	+	2.04923i
$101$	3.99029	+	3.34825i	0.397048	+	0.333163i	0.819351	−	0.573292i	$-0.194334\pi$
$101$	3.99029	+	3.34825i	0.397048	+	0.333163i	−0.422303	+	0.906455i	$0.638778\pi$
$102$	−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
$105$	5.21333	−	8.82163i	0.508769	−	0.860903i
$106$	17.2436	−	6.27615i	1.67485	−	0.609594i
$107$	14.1118			1.36424			0.682122	−	0.731238i	$-0.261057\pi$
$107$	14.1118			1.36424			0.682122	+	0.731238i	$0.261057\pi$
$108$	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	$0.590446\pi$
$110$	−3.07122	−	2.88916i	−0.292829	−	0.275471i
$111$	2.46848	+	8.50963i	0.234298	+	0.807699i
$112$	8.30229	+	16.6575i	0.784492	+	1.57399i
$113$	2.41576	+	13.7004i	0.227255	+	1.28883i	0.858326	+	0.513104i	$0.171505\pi$
$113$	2.41576	+	13.7004i	0.227255	+	1.28883i	−0.631071	+	0.775725i	$0.717384\pi$
$114$	−4.58388	+	10.3815i	−0.429320	+	0.972316i
$115$	10.5083	+	2.47446i	0.979900	+	0.230744i
$116$	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
$119$	−1.62677	+	3.73991i	−0.149125	+	0.342837i
$120$	2.99534	−	24.1372i	0.273435	−	2.20341i
$121$	−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
$125$	−10.4894	+	3.86944i	−0.938200	+	0.346093i
$126$	−17.6832	+	9.73953i	−1.57534	+	0.867666i
$127$	5.83188	+	3.36704i	0.517496	+	0.298776i	0.735909	−	0.677080i	$-0.236755\pi$
$127$	5.83188	+	3.36704i	0.517496	+	0.298776i	−0.218414	+	0.975856i	$0.570088\pi$
$128$	−9.15764	−	7.68417i	−0.809429	−	0.679191i
$129$	6.58678	−	14.9176i	0.579933	−	1.31342i
$130$	15.2513	+	20.4243i	1.33762	+	1.79133i
$131$	−3.66473	+	3.07508i	−0.320189	+	0.268671i	−0.788688	−	0.614793i	$-0.789239\pi$
$131$	−3.66473	+	3.07508i	−0.320189	+	0.268671i	0.468499	+	0.883464i	$0.344795\pi$
$132$	1.59886	+	5.51177i	0.139163	+	0.479738i
$133$	6.77188	−	0.770623i	0.587197	−	0.0668214i
$134$			33.6163i			2.90401i
$135$	11.5795	+	0.956311i	0.996607	+	0.0823061i
$136$			9.68053i			0.830099i
$137$	11.5492	−	4.20355i	0.986711	−	0.359133i	0.202265	−	0.979331i	$-0.435170\pi$
$137$	11.5492	−	4.20355i	0.986711	−	0.359133i	0.784446	+	0.620198i	$0.212948\pi$
$138$	−15.3451	−	14.7275i	−1.30626	−	1.25369i
$139$	−0.986486	−	1.17565i	−0.0836727	−	0.0997172i	0.722584	−	0.691283i	$-0.242954\pi$
$139$	−0.986486	−	1.17565i	−0.0836727	−	0.0997172i	−0.806257	+	0.591566i	$0.798510\pi$
$140$	−24.2939	+	10.4333i	−2.05321	+	0.881776i
$141$	−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
$145$	−5.96575	+	9.09911i	−0.495428	+	0.755640i
$146$	6.22983	−	35.3311i	0.515584	−	2.92402i
$147$	10.4101	+	6.21531i	0.858609	+	0.512630i
$148$	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	$-0.0344553\pi$
$150$	21.6702	+	3.94772i	1.76936	+	0.322330i
$151$	−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
$154$	3.43479	−	3.61853i	0.276783	−	0.291589i
$155$	4.18529	−	17.7736i	0.336171	−	1.42761i
$156$	−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
$160$	−8.16952	+	8.68430i	−0.645857	+	0.686555i
$161$	−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	$-0.831623\pi$
$163$		−	12.8858i		−	1.00929i	0.863326	−	0.504646i	$-0.168377\pi$
$164$	−34.5868	+	12.5886i	−2.70078	+	0.983002i
$165$	−2.79868	+	0.642319i	−0.217877	+	0.0500045i
$166$	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	$0.576648\pi$
$168$	28.5433	+	3.67236i	2.20216	+	0.283329i
$169$	5.42962	+	4.55599i	0.417663	+	0.350461i
$170$	−8.75281	−	0.497094i	−0.671310	−	0.0381254i
$171$	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
$175$	−4.52260	−	12.4317i	−0.341876	−	0.939745i
$176$	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	$0.419061\pi$
$180$	−22.6610	−	19.6279i	−1.68905	−	1.46298i
$181$	−17.4008	−	10.0463i	−1.29339	−	0.746739i	−0.314136	−	0.949378i	$-0.601715\pi$
$181$	−17.4008	−	10.0463i	−1.29339	−	0.746739i	−0.979254	+	0.202639i	$0.935048\pi$
$182$	−24.2471	+	17.9368i	−1.79732	+	1.32956i
$183$	−3.24334	−	4.43529i	−0.239755	−	0.327866i
$184$	5.26495	+	29.8590i	0.388137	+	2.20123i
$185$	10.5098	+	4.51547i	0.772696	+	0.331984i
$186$	−24.9100	+	25.9546i	−1.82649	+	1.90308i
$187$	1.07394	−	0.390883i	0.0785344	−	0.0285842i
$188$			1.32286i			0.0964792i
$189$	−1.19305	+	13.6959i	−0.0867814	+	0.996227i
$190$	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	0.744275	−	0.667873i	$-0.232795\pi$
$193$	−0.593111	−	0.706843i	−0.0426931	−	0.0508796i	−0.786968	+	0.616993i	$0.788351\pi$
$194$	1.20376	+	6.82688i	0.0864251	+	0.490141i
$195$	17.3359	−	0.886075i	1.24145	−	0.0634532i
$196$	−12.2156	−	28.8001i	−0.872546	−	2.05715i
$197$	−3.64955	+	6.32121i	−0.260020	+	0.450368i	−0.966247	−	0.257618i	$-0.917062\pi$
$197$	−3.64955	+	6.32121i	−0.260020	+	0.450368i	0.706227	+	0.707985i	$0.250396\pi$
$198$	5.39094	+	1.71499i	0.383117	+	0.121879i
$199$	7.77362	−	4.48810i	0.551057	−	0.318153i	−0.198491	−	0.980103i	$-0.563604\pi$
$199$	7.77362	−	4.48810i	0.551057	−	0.318153i	0.749548	+	0.661950i	$0.230271\pi$
$200$	−21.6139	−	22.7771i	−1.52834	−	1.61058i
$201$	19.0179	+	12.7427i	1.34142	+	0.898801i
$202$	−12.4497	−	4.53131i	−0.875955	−	0.318822i
$203$	−10.7344	−	7.10705i	−0.753407	−	0.498817i
$204$	9.91273	+	6.64190i	0.694030	+	0.465026i
$205$	−5.30721	−	17.6345i	−0.370672	−	1.23164i
$206$	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
$210$	−4.78612	+	25.6193i	−0.330274	+	1.76790i
$211$	−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
$220$	6.80730	+	2.92471i	0.458948	+	0.197184i
$221$	−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	$0.776331\pi$
$224$	−10.2319	−	9.71235i	−0.683647	−	0.648934i
$225$	10.4477	−	10.7631i	0.696515	−	0.717542i
$226$	−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	$-0.658881\pi$
$229$	6.84571	−	18.8084i	0.452377	−	1.24290i	0.931047	−	0.364900i	$-0.118897\pi$
$230$	−27.2678	+	3.22713i	−1.79799	+	0.212791i
$231$	−0.745122	−	3.31483i	−0.0490254	−	0.218100i
$232$	−30.0935	−	5.30629i	−1.97573	−	0.348375i
$233$	13.3489	+	23.1211i	0.874519	+	1.51471i	0.857275	+	0.514860i	$0.172156\pi$
$233$	13.3489	+	23.1211i	0.874519	+	1.51471i	0.0172442	+	0.999851i	$0.494511\pi$
$234$	−30.2940	−	15.8690i	−1.98038	−	1.03739i
$235$	−0.660813	−	0.0375293i	−0.0431067	−	0.00244814i
$236$	29.0035	+	24.3368i	1.88796	+	1.58419i
$237$	2.77903	+	25.6797i	0.180517	+	1.66807i
$238$	0.634678	−	10.3537i	0.0411401	−	0.671132i
$239$	−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	$-0.510188\pi$
$240$	6.09447	+	26.5545i	0.393396	+	1.71409i
$241$	1.41743	+	3.89436i	0.0913047	+	0.250858i	0.976936	−	0.213531i	$-0.0684964\pi$
$241$	1.41743	+	3.89436i	0.0913047	+	0.250858i	−0.885632	+	0.464388i	$0.846274\pi$
$242$	26.5798			1.70861
$243$	−14.5645	+	5.55648i	−0.934315	+	0.356448i
$244$			14.1774i			0.907618i
$245$	14.7332	−	5.28509i	0.941271	−	0.337652i
$246$	−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
$250$	21.7042	−	18.3730i	1.37269	−	1.16201i
$251$	−7.75081	+	13.4248i	−0.489227	+	0.847365i	−0.999923	−	0.0123956i	$-0.996054\pi$
$251$	−7.75081	+	13.4248i	−0.489227	+	0.847365i	0.510697	+	0.859761i	$0.329388\pi$
$252$	23.3442	−	26.7083i	1.47055	−	1.68246i
$253$	3.09992	−	1.78974i	0.194890	−	0.112520i
$254$	−16.8675	−	2.97420i	−1.05836	−	0.186618i
$255$	−3.59909	+	4.76333i	−0.225384	+	0.298291i
$256$	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
$259$	−5.39858	+	12.4112i	−0.335451	+	0.771197i
$260$	−37.4562	−	24.5578i	−2.32294	−	1.52301i
$261$	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	0.462171	−	0.886791i	$-0.347071\pi$
$263$	−5.36619	−	4.50276i	−0.330893	−	0.277652i	−0.793064	+	0.609139i	$0.791515\pi$
$264$	−4.76024	−	6.50965i	−0.292972	−	0.400641i
$265$	−9.65244	−	12.9264i	−0.592945	−	0.794063i
$266$	−15.5148	+	7.73274i	−0.951273	+	0.474125i
$267$	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	$-0.756568\pi$
$269$	−23.6685			−1.44309			−0.721546	+	0.692366i	$0.756568\pi$
$270$	−28.5076	+	7.78749i	−1.73492	+	0.473932i
$271$		−	3.15216i		−	0.191480i	−0.995406	−	0.0957399i	$-0.969478\pi$
$271$		−	3.15216i		−	0.191480i	0.995406	−	0.0957399i	$-0.0305217\pi$
$272$	−3.70879	−	10.1898i	−0.224878	−	0.617848i
$273$	0.956281	+	20.5166i	0.0578767	+	1.24172i
$274$	−23.9464	+	20.0934i	−1.44665	+	1.21389i
$275$	−1.65412	+	3.31751i	−0.0997472	+	0.200054i
$276$	34.1875	+	15.0953i	2.05785	+	0.908629i
$277$	−2.11219	+	2.51722i	−0.126909	+	0.151245i	−0.825757	−	0.564025i	$-0.809252\pi$
$277$	−2.11219	+	2.51722i	−0.126909	+	0.151245i	0.698848	+	0.715270i	$0.253696\pi$
$278$	3.38046	+	1.95171i	0.202747	+	0.117056i
$279$	5.24092	+	23.9309i	0.313766	+	1.43270i
$280$	27.0648	−	25.4527i	1.61743	−	1.52109i
$281$	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
$285$	9.90105	+	1.22868i	0.586488	+	0.0727810i
$286$	8.32329	+	1.46762i	0.492167	+	0.0867823i
$287$	20.8934	−	6.18580i	1.23330	−	0.365136i
$288$	4.84936	−	15.2436i	0.285751	−	0.898240i
$289$	−7.31191	+	12.6646i	−0.430112	+	0.744976i
$290$	6.34306	−	26.9370i	0.372477	−	1.58180i
$291$	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	$0.541867\pi$
$294$	−30.2874	−	5.79910i	−1.76640	−	0.338211i
$295$	−12.9799	+	13.7978i	−0.755720	+	0.803340i
$296$			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
$300$	−38.1529	+	6.50480i	−2.20276	+	0.375555i
$301$	22.2939	−	11.1115i	1.28500	−	0.640457i
$302$	−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
$305$	−7.08214	−	0.402213i	−0.405522	−	0.0230306i
$306$	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	$-0.371506\pi$
$308$	−3.49671	+	8.03888i	−0.199244	+	0.458058i
$309$	18.2608	+	1.22042i	1.03882	+	0.0694272i
$310$	5.45836	+	46.1207i	0.310014	+	2.61948i
$311$	−18.6776	−	6.79811i	−1.05911	−	0.385485i	−0.247018	−	0.969011i	$-0.579451\pi$
$311$	−18.6776	−	6.79811i	−1.05911	−	0.385485i	−0.812095	+	0.583526i	$0.801673\pi$
$312$	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
$315$	12.6795	+	12.4190i	0.714407	+	0.699731i
$316$	33.3232	−	57.7175i	1.87458	−	3.24686i
$317$	−3.01300	−	2.52821i	−0.169227	−	0.141998i	0.554241	−	0.832356i	$-0.313009\pi$
$317$	−3.01300	−	2.52821i	−0.169227	−	0.141998i	−0.723468	+	0.690358i	$0.757453\pi$
$318$	3.41961	+	31.5991i	0.191762	+	1.77199i
$319$	0.626451	+	3.55278i	0.0350745	+	0.198917i
$320$	−0.447754	+	1.04215i	−0.0250302	+	0.0582580i
$321$	−5.84010	+	23.7345i	−0.325962	+	1.32473i
$322$	−3.67344	−	32.2806i	−0.204713	−	1.79893i
$323$	−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
$329$	0.0479165	−	0.781678i	0.00264172	−	0.0430953i
$330$	6.13024	−	3.96978i	0.337459	−	0.218529i
$331$	−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
$335$	28.3000	−	8.51706i	1.54619	−	0.465337i
$336$	−31.4518	+	7.06988i	−1.71584	+	0.385694i
$337$	0.198807	−	0.546218i	0.0108297	−	0.0297544i	−0.934160	−	0.356854i	$-0.883849\pi$
$337$	0.198807	−	0.546218i	0.0108297	−	0.0297544i	0.944990	+	0.327100i	$0.106071\pi$
$338$	−16.9404	−	6.16579i	−0.921435	−	0.335375i
$339$	−24.0423	−	1.60681i	−1.30580	−	0.0872702i
$340$	14.7508	−	4.43936i	0.799976	−	0.240758i
$341$	−3.02716	−	5.24319i	−0.163930	−	0.283935i
$342$	−15.5635	−	12.0059i	−0.841575	−	0.649203i
$343$	6.17504	+	17.4605i	0.333421	+	0.942778i
$344$	38.0051	−	45.2928i	2.04910	−	2.44202i
$345$	−8.51053	+	16.6496i	−0.458191	+	0.896386i
$346$	36.7289	−	6.47629i	1.97456	−	0.348168i
$347$	−26.3941	+	22.1472i	−1.41691	+	1.18893i	−0.463934	+	0.885870i	$0.653563\pi$
$347$	−26.3941	+	22.1472i	−1.41691	+	1.18893i	−0.952973	+	0.303056i	$0.901993\pi$
$348$	−26.0810	+	27.1746i	−1.39809	+	1.45671i
$349$	−4.81070	−	13.2173i	−0.257511	−	0.707505i	−0.999319	−	0.0368933i	$-0.988254\pi$
$349$	−4.81070	−	13.2173i	−0.257511	−	0.707505i	0.741808	−	0.670612i	$-0.233968\pi$
$350$	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
$355$	−1.83723	−	0.789353i	−0.0975099	−	0.0418945i
$356$	−5.77029	−	32.7249i	−0.305824	−	1.73442i
$357$	−5.61687	−	4.28377i	−0.297276	−	0.226721i
$358$	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	$0.949417\pi$
$360$	39.3563	+	15.0268i	2.07426	+	0.791983i
$361$	−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
$364$	29.2560	−	44.1878i	1.53343	−	2.31607i
$365$	−31.3219	+	3.70693i	−1.63947	+	0.194030i
$366$	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
$370$	−29.0470	−	1.64965i	−1.51008	−	0.0857615i
$371$	15.3459	−	11.3521i	0.796718	−	0.589372i
$372$	25.5321	−	57.8247i	1.32378	−	2.99807i
$373$	−12.4167	+	2.18941i	−0.642914	+	0.113363i	−0.485594	−	0.874185i	$-0.661397\pi$
$373$	−12.4167	+	2.18941i	−0.642914	+	0.113363i	−0.157320	+	0.987548i	$0.550286\pi$
$374$	−2.22675	+	1.86846i	−0.115142	+	0.0966159i
$375$	−2.16699	−	19.2433i	−0.111903	−	0.993719i
$376$	−0.635776	−	1.74678i	−0.0327876	−	0.0900833i
$377$		−	21.8086i		−	1.12320i
$378$	−9.06270	−	33.7717i	−0.466135	−	1.73703i
$379$	2.16560			0.111239			0.0556196	−	0.998452i	$-0.482287\pi$
$379$	2.16560			0.111239			0.0556196	+	0.998452i	$0.482287\pi$
$380$	−18.7503	−	17.6388i	−0.961870	−	0.904852i
$381$	−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
$385$	−3.91650	−	1.97479i	−0.199604	−	0.100645i
$386$	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	$0.597380\pi$
$390$	−40.6629	+	17.1984i	−2.05904	+	0.870875i
$391$	2.54540	−	6.99343i	0.128726	−	0.353673i
$392$	29.9718	+	32.1585i	1.51381	+	1.62425i
$393$	−3.65530	−	7.43626i	−0.184385	−	0.375109i
$394$	3.22375	−	18.2828i	0.162410	−	0.921074i
$395$	27.8865	+	18.2836i	1.40312	+	0.919946i
$396$	−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
$399$	−1.50640	+	11.7084i	−0.0754144	+	0.586155i
$400$	31.4773	+	15.6947i	1.57387	+	0.784733i
$401$	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
$405$	−6.40052	+	19.0797i	−0.318044	+	0.948076i
$406$	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	$-0.927900\pi$
$409$	−20.7578	−	24.7382i	−1.02641	−	1.22323i	−0.0519522	−	0.998650i	$-0.516544\pi$
$410$	28.0249	+	37.5305i	1.38405	+	1.85350i
$411$	2.29034	+	21.1639i	0.112974	+	1.04394i
$412$	−36.1743	−	30.3538i	−1.78218	−	1.49543i
$413$	−16.2567	−	15.4312i	−0.799938	−	0.759320i
$414$	31.1204	−	19.7137i	1.52948	−	0.968877i
$415$	10.3411	−	15.7725i	0.507626	−	0.774243i
$416$	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	0.786918	−	0.617058i	$-0.211675\pi$
$419$	20.3282	+	7.39884i	0.993095	+	0.361457i	0.206177	+	0.978515i	$0.433898\pi$
$420$	−7.49376	−	45.1773i	−0.365658	−	2.20443i
$421$	−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
$425$	1.79914	+	7.49451i	0.0872711	+	0.363537i
$426$	2.32540	+	3.18000i	0.112666	+	0.154072i
$427$	0.513536	−	8.37748i	0.0248517	−	0.405414i
$428$	48.3123	−	40.5388i	2.33526	−	1.95952i
$429$	3.98533	−	4.15245i	0.192414	−	0.200482i
$430$	39.0006	+	36.6887i	1.88078	+	1.76929i
$431$		−	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	$0.626074\pi$
$434$	−54.5993	+	6.21325i	−2.62085	+	0.298246i
$435$	−12.8348	−	13.7993i	−0.615380	−	0.661626i
$436$	−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	−0.829741	−	0.558149i	$-0.811512\pi$
$439$	−2.84928	+	3.39564i	−0.135989	+	0.162065i	0.693752	+	0.720214i	$0.255956\pi$
$440$	−10.3944	−	0.590325i	−0.495534	−	0.0281427i
$441$	−14.7616	+	14.9364i	−0.702932	+	0.711257i
$442$	15.2181	−	8.78615i	0.723849	−	0.417915i
$443$	0.934802	−	5.30152i	0.0444138	−	0.251883i	−0.954515	−	0.298164i	$-0.903626\pi$
$443$	0.934802	−	5.30152i	0.0444138	−	0.251883i	0.998928	+	0.0462809i	$0.0147369\pi$
$444$	32.8964	+	22.0418i	1.56119	+	1.04606i
$445$	16.5110	−	1.95406i	0.782694	−	0.0926313i
$446$	12.0757	+	4.39520i	0.571801	+	0.208119i
$447$	15.5104	+	10.3926i	0.733618	+	0.491551i
$448$	−1.23070	−	0.535322i	−0.0581450	−	0.0252916i
$449$	−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	$0.470034\pi$
$450$	−15.6077	+	34.8130i	−0.735753	+	1.64110i
$451$	−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
$455$	21.2434	+	15.8680i	0.995906	+	0.743903i
$456$	7.80638	+	26.9110i	0.365567	+	1.26022i
$457$	7.74361	+	21.2754i	0.362231	+	0.995221i	0.978239	+	0.207481i	$0.0665267\pi$
$457$	7.74361	+	21.2754i	0.362231	+	0.995221i	−0.616008	+	0.787740i	$0.711251\pi$
$458$			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	−0.767296	−	0.641294i	$-0.778398\pi$
$461$	−20.2441	+	7.36826i	−0.942863	+	0.343174i	−0.175567	+	0.984467i	$0.556176\pi$
$462$	4.66448	+	7.27443i	0.217011	+	0.338437i
$463$	−21.4013	−	25.5051i	−0.994604	−	1.18532i	−0.982664	−	0.185395i	$-0.940644\pi$
$463$	−21.4013	−	25.5051i	−0.994604	−	1.18532i	−0.0119402	−	0.999929i	$-0.503801\pi$
$464$	33.7096	−	5.94390i	1.56493	−	0.275939i
$465$	28.1611	+	14.3947i	1.30594	+	0.667537i
$466$	−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
$469$	9.92703	+	33.5299i	0.458388	+	1.54827i
$470$	1.61203	−	0.485150i	0.0743572	−	0.0223783i
$471$	−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
$475$	9.34315	−	8.86602i	0.428693	−	0.406801i
$476$	5.17428	+	17.4768i	0.237163	+	0.801050i
$477$	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	0.825167	−	0.564889i	$-0.191081\pi$
$479$	9.02032	+	7.56895i	0.412149	+	0.345834i	−0.413018	+	0.910723i	$0.635525\pi$
$480$	−11.2251	−	17.3341i	−0.512353	−	0.791191i
$481$	−22.5794	+	3.98136i	−1.02953	+	0.181534i
$482$	−6.77547	−	8.07469i	−0.308614	−	0.367792i
$483$	−19.6547	−	10.1582i	−0.894319	−	0.462213i
$484$	−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	$-0.752387\pi$
$487$		−	30.9740i		−	1.40357i	0.712390	−	0.701784i	$-0.247613\pi$
$488$	−6.81380	−	18.7208i	−0.308446	−	0.847450i
$489$	21.6724	+	5.33270i	0.980060	+	0.241153i
$490$	−30.6156	+	25.4482i	−1.38307	+	1.14963i
$491$	−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
$495$	0.0779105	−	4.97288i	0.00350182	−	0.223514i
$496$	−49.7486	+	28.7224i	−2.23378	+	1.28967i
$497$	0.943730	−	2.16962i	0.0423321	−	0.0973208i
$498$	−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	$0.542725\pi$
$500$	−24.7950	+	43.3798i	−1.10887	+	1.94000i
$501$	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	$0.620704\pi$
$504$	−17.9889	+	46.4867i	−0.801291	+	2.07068i
$505$	−0.660431	+	11.6288i	−0.0293888	+	0.517476i
$506$	−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	−0.522092	−	0.852889i	$-0.674848\pi$
$509$	5.12539	−	4.30071i	0.227179	−	0.190626i	0.749271	+	0.662263i	$0.230404\pi$
$510$	4.45835	−	14.5155i	0.197419	−	0.642757i
$511$	−4.21960	−	37.0799i	−0.186664	−	1.64032i
$512$	−50.8452			−2.24706
$513$	−12.6917	+	4.25380i	−0.560350	+	0.187810i
$514$			71.8296i			3.16827i
$515$	16.1891	−	17.2092i	0.713376	−	0.758328i
$516$	−20.3035	−	69.9925i	−0.893812	−	3.08125i
$517$	−0.168113	+	0.141064i	−0.00739362	+	0.00620398i
$518$	2.10624	−	34.3598i	0.0925429	−	1.50968i
$519$	10.2587	−	23.2337i	0.450307	−	1.01985i
$520$	61.2622	+	14.4259i	2.68652	+	0.632616i
$521$	12.5760	−	21.7822i	0.550963	−	0.954296i	−0.447242	−	0.894413i	$-0.647594\pi$
$521$	12.5760	−	21.7822i	0.550963	−	0.954296i	0.998205	−	0.0598833i	$-0.0190729\pi$
$522$	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
$525$	22.7803	−	2.46172i	0.994212	−	0.107438i
$526$	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
$530$	34.3146	+	22.4981i	1.49053	+	0.977254i
$531$	7.70478	−	24.2194i	0.334359	−	1.05103i
$532$	20.9700	−	22.0917i	0.909163	−	0.957796i
$533$	28.2765	+	23.7268i	1.22479	+	1.02772i
$534$	−29.9649	−	13.2308i	−1.29671	−	0.572554i
$535$	18.8800	+	25.2838i	0.816252	+	1.09311i
$536$	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
$540$	42.3900	−	29.9903i	1.82417	−	1.29058i
$541$	−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
$545$	−7.83141	−	10.4877i	−0.335461	−	0.449244i
$546$	−20.1331	−	48.2039i	−0.861618	−	2.06294i
$547$	−11.6827	+	13.9229i	−0.499517	+	0.595301i	−0.955611	−	0.294631i	$-0.904803\pi$
$547$	−11.6827	+	13.9229i	−0.499517	+	0.595301i	0.456095	+	0.889931i	$0.349248\pi$
$548$	27.4634	−	47.5679i	1.17318	−	2.03200i
$549$	8.80188	−	3.61941i	0.375655	−	0.154473i
$550$	1.06750	−	9.36797i	0.0455185	−	0.399451i
$551$	2.17664	−	12.3443i	0.0927279	−	0.525886i
$552$	−52.3982	−	3.50192i	−2.23022	−	0.149052i
$553$	−21.7814	+	32.8983i	−0.926238	+	1.39898i
$554$	2.85851	−	7.85369i	0.121446	−	0.333671i
$555$	−11.9439	+	15.8076i	−0.506991	+	0.670994i
$556$	−6.75452	−	1.19100i	−0.286455	−	0.0505098i
$557$	−15.4918	−	26.8326i	−0.656409	−	1.13693i	−0.981539	−	0.191264i	$-0.938741\pi$
$557$	−15.4918	−	26.8326i	−0.656409	−	1.13693i	0.325130	−	0.945669i	$-0.394592\pi$
$558$	−33.3437	−	52.6369i	−1.41155	−	2.22830i
$559$	36.5438	+	21.0985i	1.54564	+	0.892373i
$560$	−18.7373	+	37.1607i	−0.791794	+	1.57033i
$561$	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
$565$	−21.3147	+	22.6578i	−0.896715	+	0.953220i
$566$	−13.6857			−0.575255
$567$	−22.5411	−	7.67451i	−0.946638	−	0.322299i
$568$		−	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	$-0.231872\pi$
$570$	−24.7329	+	5.67639i	−1.03595	+	0.237758i
$571$	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
$574$	−44.5552	+	32.9597i	−1.85970	+	1.37571i
$575$	9.62537	+	22.1378i	0.401406	+	0.923212i
$576$	−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
$580$	5.71493	+	48.2887i	0.237300	+	2.00508i
$581$	18.6072	+	12.3195i	0.771956	+	0.511098i
$582$	−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
$585$	−5.68407	+	29.5236i	−0.235007	+	1.22065i
$586$	−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	$0.356328\pi$
$588$	53.4938	−	8.62656i	2.20605	−	0.355753i
$589$	3.65287	+	20.7165i	0.150514	+	0.853607i
$590$	19.0198	−	44.2689i	0.783035	−	1.82252i
$591$	−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	$0.574206\pi$
$600$	47.2532	−	26.9260i	1.92910	−	1.09925i
$601$	1.26699	−	1.50994i	0.0516817	−	0.0615918i	−0.739584	−	0.673064i	$-0.764978\pi$
$601$	1.26699	−	1.50994i	0.0516817	−	0.0615918i	0.791266	+	0.611472i	$0.209422\pi$
$602$	−43.6175	+	45.9507i	−1.77772	+	1.87281i
$603$	−29.3022	+	26.7124i	−1.19328	+	1.08781i
$604$	0.973029	+	1.68534i	0.0395920	+	0.0685754i
$605$	−6.73427	−	22.3762i	−0.273787	−	0.909723i
$606$	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
$609$	16.3956	−	15.1128i	0.664383	−	0.612402i
$610$	17.2766	−	5.19950i	0.699508	−	0.210522i
$611$	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	0.515873	−	0.856665i	$-0.327468\pi$
$613$	0.790195	+	0.456219i	0.0319157	+	0.0184265i	−0.483957	+	0.875092i	$0.660801\pi$
$614$	40.9674	+	34.3757i	1.65331	+	1.38729i
$615$	31.8555	−	1.62820i	1.28454	−	0.0656555i
$616$	0.753714	−	12.2956i	0.0303680	−	0.495403i
$617$	−11.4019	+	9.56731i	−0.459022	+	0.385165i	−0.842771	−	0.538272i	$-0.819077\pi$
$617$	−11.4019	+	9.56731i	−0.459022	+	0.385165i	0.383749	+	0.923437i	$0.374633\pi$
$618$	−44.7059	+	12.9683i	−1.79833	+	0.521663i
$619$	−1.40271	−	3.85392i	−0.0563798	−	0.154902i	0.908305	−	0.418308i	$-0.137377\pi$
$619$	−1.40271	−	3.85392i	−0.0563798	−	0.154902i	−0.964685	+	0.263405i	$0.915154\pi$
$620$	−36.7295	−	72.8715i	−1.47509	−	2.92659i
$621$	0.643852	−	25.0786i	0.0258369	−	1.00637i
$622$	50.5543			2.02704
$623$	2.22431	+	19.5462i	0.0891150	+	0.783102i
$624$	−39.3994	−	37.8137i	−1.57724	−	1.51376i
$625$	−20.9663	−	13.6167i	−0.838652	−	0.544667i
$626$	−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
$630$	−41.1080	−	18.6521i	−1.63778	−	0.743116i
$631$	−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
$635$	1.76974	+	14.9535i	0.0702298	+	0.593411i
$636$	−24.6362	−	50.1194i	−0.976889	−	1.98736i
$637$	−18.8880	+	25.0510i	−0.748369	+	0.992555i
$638$	−4.58784	−	7.94637i	−0.181634	−	0.314600i
$639$	2.68051	−	0.110139i	0.106039	−	0.00435704i
$640$	1.51568	−	26.6880i	0.0599124	−	1.05493i
$641$	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	$0.882863\pi$
$644$	25.4649	+	51.0921i	1.00346	+	2.01331i
$645$	35.5397	−	8.15664i	1.39938	−	0.321167i
$646$	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
$650$	−16.1892	+	54.6504i	−0.634992	+	2.14357i
$651$	−17.1815	+	33.2439i	−0.673396	+	1.30293i
$652$	−37.0167	−	44.1148i	−1.44969	−	1.72767i
$653$	−1.09581	−	6.21463i	−0.0428823	−	0.243197i	0.955831	−	0.293918i	$-0.0949593\pi$
$653$	−1.09581	−	6.21463i	−0.0428823	−	0.243197i	−0.998713	+	0.0507207i	$0.983848\pi$
$654$	2.77447	+	25.6376i	0.108490	+	1.00251i
$655$	−10.4125	−	2.45191i	−0.406850	−	0.0958040i
$656$	−28.9678	+	50.1737i	−1.13100	+	1.95895i
$657$	35.7473	−	22.6447i	1.39463	−	0.883454i
$658$	0.565465	+	1.90993i	0.0220441	+	0.0744570i
$659$	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	$0.479082\pi$
$660$	−7.73619	+	10.2387i	−0.301131	+	0.398541i
$661$	−13.5224	+	37.1526i	−0.525962	+	1.44507i	0.337823	+	0.941210i	$0.390309\pi$
$661$	−13.5224	+	37.1526i	−0.525962	+	1.44507i	−0.863785	+	0.503860i	$0.831913\pi$
$662$	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
$665$	10.4407	+	11.1020i	0.404872	+	0.430516i
$666$	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
$670$	−60.2293	+	44.9746i	−2.32686	+	1.73752i
$671$	−1.80172	+	1.51182i	−0.0695547	+	0.0583633i
$672$	20.5695	−	13.1895i	0.793484	−	0.508794i
$673$	11.7036	+	32.1553i	0.451139	+	1.23949i	0.931923	+	0.362655i	$0.118130\pi$
$673$	11.7036	+	32.1553i	0.451139	+	1.23949i	−0.480784	+	0.876839i	$0.659648\pi$
$674$			1.47843i			0.0569471i
$675$	13.7786	+	22.0261i	0.530339	+	0.847785i
$676$	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
$679$	3.21667	+	6.45385i	0.123444	+	0.247676i
$680$	−17.3443	+	12.9514i	−0.665124	+	0.496663i
$681$	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	−0.858995	−	0.511984i	$-0.828911\pi$
$683$	0.363116	−	0.628935i	0.0138942	−	0.0240655i	0.872889	+	0.487919i	$0.162244\pi$
$684$	32.9125	+	10.4703i	1.25844	+	0.400340i
$685$	22.9827	+	15.0684i	0.878125	+	0.575735i
$686$	−29.9477	−	36.3598i	−1.14341	−	1.38822i
$687$	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
$690$	5.85696	−	47.1969i	0.222971	−	1.79675i
$691$	−27.8464	−	4.91007i	−1.05933	−	0.186788i	−0.383269	−	0.923637i	$-0.625202\pi$
$691$	−27.8464	−	4.91007i	−1.05933	−	0.186788i	−0.676057	+	0.736849i	$0.736313\pi$
$692$	−56.7525	+	32.7660i	−2.15740	+	1.24558i
$693$	5.88352	+	0.118611i	0.223496	+	0.00450566i
$694$	43.8171	−	75.8935i	1.66328	−	2.88088i
$695$	0.786573	−	3.34033i	0.0298364	−	0.126706i
$696$	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
$700$	−51.1954	−	29.5681i	−1.93500	−	1.11757i
$701$			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
$705$	0.336593	−	1.09588i	0.0126768	−	0.0412732i
$706$	54.9940	+	65.5393i	2.06973	+	2.46661i
$707$	−13.7558	−	0.843223i	−0.517339	−	0.0317126i
$708$	−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	$0.457382\pi$
$710$	5.07774	+	0.288378i	0.190564	+	0.0108226i
$711$	−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
$714$	17.1511	+	5.35227i	0.641863	+	0.200304i
$715$	−0.873278	−	7.37882i	−0.0326587	−	0.275952i
$716$	−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	0.976609	−	0.215022i	$-0.0689823\pi$
$719$	8.10030	+	14.0301i	0.302090	+	0.523235i	−0.674519	+	0.738257i	$0.735649\pi$
$720$	−47.1838	−	0.739232i	−1.75844	−	0.0275496i
$721$	20.2760	+	19.2464i	0.755116	+	0.716775i
$722$	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
$725$	−24.2840	+	1.48487i	−0.901887	+	0.0551466i
$726$	−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
$735$	2.79166	+	26.9668i	0.102972	+	0.994684i
$736$	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	$0.615790\pi$
$740$	48.9521	−	14.7325i	1.79951	−	0.541576i
$741$	−17.9468	+	8.82176i	−0.659292	+	0.324076i
$742$	−26.8022	+	40.4816i	−0.983938	+	1.48613i
$743$	−16.1789	−	5.88865i	−0.593547	−	0.216033i	0.0277417	−	0.999615i	$-0.491168\pi$
$743$	−16.1789	−	5.88865i	−0.593547	−	0.216033i	−0.621289	+	0.783582i	$0.713391\pi$
$744$	−5.92314	+	88.6262i	−0.217153	+	3.24919i
$745$	23.0806	−	6.94626i	0.845608	−	0.254491i
$746$	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
$749$	−30.0162	+	22.2045i	−1.09677	+	0.811334i
$750$	21.9191	+	44.1074i	0.800373	+	1.61057i
$751$	−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
$756$	35.2594	+	50.3154i	1.28237	+	1.82995i
$757$			0.611591i			0.0222287i	0.999938	+	0.0111143i	$0.00353788\pi$
$757$			0.611591i			0.0222287i	−0.999938	+	0.0111143i	$0.996462\pi$
$758$	−5.17589	+	1.88387i	−0.187997	+	0.0684252i
$759$	1.72725	+	5.95437i	0.0626953	+	0.216130i
$760$	33.2364	+	14.2798i	1.20561	+	0.517983i
$761$	−4.86072	−	27.5665i	−0.176201	−	0.999284i	−0.936749	−	0.350003i	$-0.886181\pi$
$761$	−4.86072	−	27.5665i	−0.176201	−	0.999284i	0.760548	−	0.649282i	$-0.224930\pi$
$762$	11.9828	−	27.1384i	0.434090	−	0.983119i
$763$	12.4507	−	9.21042i	0.450747	−	0.333440i
$764$	27.4164	+	15.8289i	0.991892	+	0.572669i
$765$	−6.52191	−	8.02452i	−0.235800	−	0.290127i
$766$	−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	$-0.771638\pi$
$769$	6.83039	−	18.7663i	0.246310	−	0.676731i	0.999814	−	0.0192880i	$-0.00613994\pi$
$770$	11.0785	+	1.31286i	0.399243	+	0.0473122i
$771$	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
$775$	37.4439	−	16.2803i	1.34502	−	0.584806i
$776$	13.1118	+	11.0021i	0.470686	+	0.394953i
$777$	−18.6401	−	14.2161i	−0.668710	−	0.509999i
$778$	12.9453	−	2.28261i	0.464112	−	0.0818354i
$779$	13.6373	+	16.2522i	0.488605	+	0.582297i
$780$	56.8044	−	52.8339i	2.03392	−	1.89176i
$781$	−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
$785$	−25.6575	+	27.2743i	−0.915756	+	0.973461i
$786$	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
$790$	−82.5553	−	19.4399i	−2.93719	−	0.691642i
$791$	−26.6955	−	25.3400i	−0.949183	−	0.900987i
$792$	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
$795$	25.7353	−	10.8848i	0.912738	−	0.386043i
$796$	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	$0.774466\pi$
$798$	−6.58489	−	29.2942i	−0.233102	−	1.03700i
$799$	−0.0792325	+	0.449350i	−0.00280304	+	0.0158969i
$800$	−26.4892	−	3.01852i	−0.936536	−	0.106721i
$801$	−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
$805$	−26.2447	+	11.2711i	−0.925006	+	0.397255i
$806$	−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	$0.963923\pi$
$810$	−1.29998	−	51.1693i	−0.0456766	−	1.79790i
$811$		−	11.0500i		−	0.388018i	−0.981000	−	0.194009i	$-0.937851\pi$
$811$		−	11.0500i		−	0.388018i	0.981000	−	0.194009i	$-0.0621491\pi$
$812$	−57.1658	+	6.50531i	−2.00612	+	0.228292i
$813$	5.30156	+	1.30450i	0.185934	+	0.0457508i
$814$	−7.38967	+	6.20067i	−0.259008	+	0.217333i
$815$	23.0871	−	17.2396i	0.808705	−	0.603878i
$816$	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
$819$	−34.9023	−	6.88231i	−1.21958	−	0.240487i
$820$	−68.8275	−	45.1261i	−2.40356	−	1.57587i
$821$	−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	$0.245030\pi$
$823$	−8.01468	+	22.0202i	−0.279374	+	0.767575i	−0.997434	+	0.0715930i	$0.977192\pi$
$824$	62.3551	+	22.6954i	2.17224	+	0.790631i
$825$	−4.89513	−	4.15497i	−0.170426	−	0.144658i
$826$	52.2780	+	22.7396i	1.81898	+	0.791212i
$827$	10.8253	+	18.7500i	0.376433	+	0.652001i	0.990540	−	0.137222i	$-0.0438173\pi$
$827$	10.8253	+	18.7500i	0.376433	+	0.652001i	−0.614108	+	0.789222i	$0.710484\pi$
$828$	−39.5368	+	51.2524i	−1.37400	+	1.78114i
$829$	11.7660	+	6.79310i	0.408650	+	0.235934i	0.690209	−	0.723610i	$-0.257518\pi$
$829$	11.7660	+	6.79310i	0.408650	+	0.235934i	−0.281560	+	0.959544i	$0.590852\pi$
$830$	−10.9952	+	46.6930i	−0.381648	+	1.62074i
$831$	−3.35955	−	4.59420i	−0.116541	−	0.159371i
$832$	−0.394791	−	2.23897i	−0.0136869	−	0.0776224i
$833$	−2.42445	−	10.5145i	−0.0840020	−	0.364306i
$834$	−4.68153	+	4.87784i	−0.162108	+	0.168906i
$835$	−16.9846	−	15.9778i	−0.587778	−	0.552935i
$836$	−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	−0.339143	−	0.940735i	$-0.610137\pi$
$839$	0.166559	−	0.0606223i	0.00575024	−	0.00209292i	0.344894	+	0.938642i	$0.387915\pi$
$840$	31.6078	+	56.0533i	1.09057	+	1.93402i
$841$	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
$845$	−0.898654	+	15.8235i	−0.0309146	+	0.544343i
$846$	−1.66911	+	1.52160i	−0.0573853	+	0.0523136i
$847$	26.5114	−	7.84911i	0.910943	−	0.269699i
$848$	−8.81313	+	49.9818i	−0.302644	+	1.71638i
$849$	−5.18776	+	7.74249i	−0.178043	+	0.265722i
$850$	−10.8196	−	16.3472i	−0.371108	−	0.560704i
$851$	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	$-0.0507175\pi$
$854$	6.06026	+	20.4693i	0.207378	+	0.700446i
$855$	−6.16399	+	16.1439i	−0.210804	+	0.552111i
$856$	−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	0.451475	−	0.892284i	$-0.350898\pi$
$859$	34.6107	−	6.10280i	1.18090	−	0.208225i	0.729426	+	0.684059i	$0.239787\pi$
$860$	−86.4441	−	37.1402i	−2.94772	−	1.26647i
$861$	1.75721	+	37.7002i	0.0598855	+	1.28482i
$862$	19.7241	+	54.1915i	0.671805	+	1.84577i
$863$	29.6880			1.01059			0.505296	−	0.862946i	$-0.331383\pi$
$863$	29.6880			1.01059			0.505296	+	0.862946i	$0.331383\pi$
$864$	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
$868$	86.4170	−	43.0712i	2.93318	−	1.46193i
$869$	10.8884	−	1.91992i	0.369364	−	0.0651288i
$870$	42.6799	+	21.8160i	1.44698	+	0.739632i
$871$	−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
$875$	16.2227	−	24.7351i	0.548428	−	0.836198i
$876$	−108.942	−	7.28092i	−3.68082	−	0.245999i
$877$	7.95670	−	21.8609i	0.268679	−	0.738189i	−0.729832	−	0.683627i	$-0.760402\pi$
$877$	7.95670	−	21.8609i	0.268679	−	0.738189i	0.998510	−	0.0545619i	$-0.0173762\pi$
$878$	3.85603	−	10.5944i	0.130135	−	0.357542i
$879$	−35.9265	+	17.6597i	−1.21177	+	0.595647i
$880$	11.1674	−	3.36091i	0.376453	−	0.113296i
$881$	21.4076	+	37.0791i	0.721241	+	1.24923i	0.960502	+	0.278272i	$0.0897615\pi$
$881$	21.4076	+	37.0791i	0.721241	+	1.24923i	−0.239261	+	0.970955i	$0.576905\pi$
$882$	22.2877	−	48.5400i	0.750465	−	1.63443i
$883$	−46.5253	−	26.8614i	−1.56570	−	0.903959i	−0.996661	−	0.0816501i	$-0.973981\pi$
$883$	−46.5253	−	26.8614i	−1.56570	−	0.903959i	−0.569042	−	0.822309i	$-0.692686\pi$
$884$	−19.8470	+	23.6527i	−0.667525	+	0.795526i
$885$	−17.8347	−	27.5408i	−0.599506	−	0.925775i
$886$	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
$889$	−17.7024	+	2.01449i	−0.593721	+	0.0675639i
$890$	−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
$895$	−14.6274	−	6.28457i	−0.488940	−	0.210070i
$896$	31.5692	+	1.93518i	1.05465	+	0.0646499i
$897$	−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
$900$	4.84902	−	66.8608i	0.161634	−	2.22869i
$901$	−9.63143	+	5.56071i	−0.320869	+	0.185254i
$902$	15.2944	+	2.69682i	0.509249	+	0.0897943i
$903$	9.46211	+	42.0941i	0.314879	+	1.40080i
$904$	−82.0972	−	29.8809i	−2.73051	−	0.993825i
$905$	−5.28042	−	44.6172i	−0.175527	−	1.48313i
$906$	1.91404	+	0.127921i	0.0635897	+	0.00424988i
$907$	14.9941	+	2.64387i	0.497873	+	0.0877884i	0.416945	−	0.908932i	$-0.363101\pi$
$907$	14.9941	+	2.64387i	0.497873	+	0.0877884i	0.0809274	+	0.996720i	$0.474212\pi$
$908$	−51.2484	+	29.5883i	−1.70074	+	0.981921i
$909$	−5.94305	−	14.4526i	−0.197119	−	0.479363i
$910$	−64.5766	−	19.4455i	−2.14069	−	0.644613i
$911$	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
$915$	3.60737	−	11.7449i	0.119256	−	0.388274i
$916$	−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	$0.431078\pi$
$920$	−46.4536	+	49.3808i	−1.53153	+	1.62804i
$921$	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
$924$	−12.0734	−	9.20790i	−0.397185	−	0.302918i
$925$	5.97062	+	24.8713i	0.196313	+	0.817762i
$926$	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	$0.299585\pi$
$929$	−7.34332	+	41.6461i	−0.240927	+	1.36636i	−0.829765	+	0.558112i	$0.811526\pi$
$930$	−79.8287	−	9.90645i	−2.61768	−	0.324845i
$931$	−13.1914	+	12.2944i	−0.432330	+	0.402934i
$932$	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
$935$	2.13714	+	1.40119i	0.0698919	+	0.0458240i
$936$	−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	$0.275730\pi$
$938$	−52.8940	−	71.5026i	−1.72705	−	2.33464i
$939$	−35.0036	−	15.4556i	−1.14230	−	0.504375i
$940$	−2.37012	+	1.76982i	−0.0773048	+	0.0577252i
$941$	−3.07590	+	2.58099i	−0.100271	+	0.0841378i	−0.691545	−	0.722333i	$-0.743070\pi$
$941$	−3.07590	+	2.58099i	−0.100271	+	0.0841378i	0.591274	+	0.806471i	$0.298625\pi$
$942$	70.8529	−	20.5531i	2.30851	−	0.669656i
$943$	−37.3642	+	13.5994i	−1.21674	+	0.442859i
$944$	59.5959			1.93968
$945$	−26.1346	+	16.1859i	−0.850159	+	0.526526i
$946$	17.7538			0.577227
$947$	−9.57429	+	3.48476i	−0.311123	+	0.113239i	−0.492862	−	0.870107i	$-0.664049\pi$
$947$	−9.57429	+	3.48476i	−0.311123	+	0.113239i	0.181740	+	0.983347i	$0.441827\pi$
$948$	83.2835	+	79.9318i	2.70492	+	2.59606i
$949$	48.4289	−	40.6367i	1.57207	−	1.31912i
$950$	−14.6180	+	29.3180i	−0.474271	+	0.951200i
$951$	5.49907	−	4.02124i	0.178320	−	0.130398i
$952$	−15.2320	−	20.5907i	−0.493671	−	0.667348i
$953$	13.5411	−	23.4539i	0.438639	−	0.759745i	−0.558946	−	0.829204i	$-0.688794\pi$
$953$	13.5411	−	23.4539i	0.438639	−	0.759745i	0.997585	+	0.0694593i	$0.0221274\pi$
$954$	−54.5611	−	7.32567i	−1.76648	−	0.237177i
$955$	−8.68489	+	13.2464i	−0.281037	+	0.428644i
$956$	−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
$959$	−17.9512	+	27.1132i	−0.579673	+	0.875531i
$960$	−1.56748	−	1.18436i	−0.0505901	−	0.0382250i
$961$	−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
$965$	0.472917	−	2.00833i	0.0152237	−	0.0646504i
$966$	55.8124	+	7.18079i	1.79573	+	0.231038i
$967$	−6.31273	+	1.11310i	−0.203004	+	0.0357950i	−0.274225	−	0.961666i	$-0.588421\pi$
$967$	−6.31273	+	1.11310i	−0.203004	+	0.0357950i	0.0712216	+	0.997461i	$0.477310\pi$
$968$	50.2739	−	42.1848i	1.61587	−	1.35587i
$969$	1.64335	−	6.67868i	0.0527920	−	0.214550i
$970$	−10.6210	+	11.2903i	−0.341020	+	0.362509i
$971$	5.57738			0.178987			0.0894933	−	0.995987i	$-0.471475\pi$
$971$	5.57738			0.178987			0.0894933	+	0.995987i	$0.471475\pi$
$972$	−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
$975$	24.7809	+	29.8747i	0.793623	+	0.956756i
$976$	14.3445	+	17.0951i	0.459157	+	0.547202i
$977$	−0.534760	−	3.03277i	−0.0171085	−	0.0970270i	0.975058	−	0.221951i	$-0.0712425\pi$
$977$	−0.534760	−	3.03277i	−0.0171085	−	0.0970270i	−0.992166	+	0.124924i	$0.960131\pi$
$978$	−56.4371	+	6.10756i	−1.80466	+	0.195298i
$979$	3.54348	−	4.22296i	0.113250	−	0.134966i
$980$	35.2572	−	60.4174i	1.12625	−	1.92996i
$981$	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
$985$	−16.2082	+	1.91823i	−0.516436	+	0.0611198i
$986$	−17.9271	−	6.52491i	−0.570914	−	0.207796i
$987$	1.29486	+	0.404082i	0.0412159	+	0.0128621i
$988$	50.8150	+	8.96006i	1.61664	+	0.285058i
$989$	−39.3650	+	22.7274i	−1.25174	+	0.722690i
$990$	4.13974	+	11.9532i	0.131570	+	0.379898i
$991$	−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
$994$	−0.368194	+	6.00647i	−0.0116784	+	0.190514i
$995$	18.4413	+	7.92321i	0.584630	+	0.251183i
$996$	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.209.7	yes	816
5.4	even	2	inner	945.2.cs.b.209.130	yes	816
7.6	odd	2	inner	945.2.cs.b.209.8	yes	816
27.23	odd	18	inner	945.2.cs.b.104.129	yes	816
35.34	odd	2	inner	945.2.cs.b.209.129	yes	816
135.104	odd	18	inner	945.2.cs.b.104.8	yes	816
189.104	even	18	inner	945.2.cs.b.104.130	yes	816
945.104	even	18	inner	945.2.cs.b.104.7	✓	816

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

\(f(q)\)	\(=\)	\(q+(-2.39005 + 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(1.33788 + 1.79167i) q^{5} +(-0.473977 - 4.37980i) q^{6} +(-2.12702 + 1.57346i) q^{7} +(-3.14000 + 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +O(q^{10})\)	\(q+(-2.39005 + 0.869908i) q^{2} +(-0.413843 + 1.68188i) q^{3} +(3.42352 - 2.87268i) q^{4} +(1.33788 + 1.79167i) q^{5} +(-0.473977 - 4.37980i) q^{6} +(-2.12702 + 1.57346i) q^{7} +(-3.14000 + 5.43864i) q^{8} +(-2.65747 - 1.39207i) q^{9} +(-4.75619 - 3.11835i) q^{10} +(0.730141 + 0.128744i) q^{11} +(3.41471 + 6.94681i) q^{12} +(-4.21165 - 1.53292i) q^{13} +(3.71492 - 5.61097i) q^{14} +(-3.56705 + 1.50869i) 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} +(9.72715 + 2.29053i) q^{20} +(-1.76613 - 4.22857i) q^{21} +(-1.85707 + 0.327452i) q^{22} +(3.69844 - 3.10336i) q^{23} +(-7.84769 - 7.53185i) q^{24} +(-1.42016 + 4.79407i) q^{25} +11.3996 q^{26} +(3.44108 - 3.89345i) q^{27} +(-2.76185 + 11.4970i) q^{28} +(1.66423 + 4.57243i) q^{29} +(7.21302 - 6.70885i) 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} +(-5.66482 - 1.70581i) 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} +(-13.9452 + 1.65040i) q^{40} +(-7.73911 - 2.81680i) q^{41} +(7.89961 + 8.57013i) q^{42} +(-9.27186 - 1.63488i) q^{43} +(2.86949 - 1.65670i) q^{44} +(-1.06124 - 6.62373i) q^{45} +(-6.13983 + 10.6345i) q^{46} +(-0.190266 + 0.226750i) q^{47} +(11.1461 + 4.92150i) q^{48} +(2.04843 - 6.69357i) q^{49} +(-0.776154 - 12.6935i) 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} +(-1.87865 - 16.5088i) q^{56} +(3.08956 - 3.21912i) q^{57} +(-7.95519 - 9.48063i) q^{58} +(1.47111 + 8.34311i) q^{59} +(-7.87792 + 15.4120i) q^{60} +(-2.03914 + 2.43015i) q^{61} +(17.9872 + 10.3849i) q^{62} +(7.84286 - 1.22046i) q^{63} +(0.253630 + 0.439300i) q^{64} +(-2.88821 - 9.59675i) 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} +(15.0231 - 0.850892i) 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} +(-7.47535 - 4.37254i) q^{75} +(-11.3377 + 1.99914i) q^{76} +(-1.75560 + 0.875009i) 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} +(-18.1937 - 9.40309i) q^{84} +(3.16694 + 1.36066i) 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} +(8.29845 + 14.9079i) q^{90} +(11.3703 - 3.36634i) q^{91} +(3.74674 - 21.2488i) q^{92} +(12.6933 - 6.23942i) q^{93} +(0.257494 - 0.707458i) q^{94} +(-0.676994 - 5.72030i) q^{95} +(-9.21497 - 0.615862i) q^{96} +(0.473281 - 2.68411i) q^{97} +(0.926942 + 17.7799i) 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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