LMFDB - Embedded newform 165.2.r.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(29,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("165.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	165.29
Dual form			165.2.r.a.74.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.875212 - 1.20463i) q^{2} +(0.577976 + 1.63277i) q^{3} +(-0.0670941 - 0.206494i) q^{4} +(0.145586 - 2.23132i) q^{5} +(2.47273 + 0.732776i) q^{6} +(0.259482 + 0.798604i) q^{7} +(2.52478 + 0.820350i) q^{8} +(-2.33189 + 1.88741i) q^{9} +O(q^{10})$	\(q+(0.875212 - 1.20463i) q^{2} +(0.577976 + 1.63277i) q^{3} +(-0.0670941 - 0.206494i) q^{4} +(0.145586 - 2.23132i) q^{5} +(2.47273 + 0.732776i) q^{6} +(0.259482 + 0.798604i) q^{7} +(2.52478 + 0.820350i) q^{8} +(-2.33189 + 1.88741i) q^{9} +(-2.56049 - 2.12826i) q^{10} +(-2.11726 - 2.55289i) q^{11} +(0.298379 - 0.228898i) q^{12} +(1.96978 + 1.43113i) q^{13} +(1.18912 + 0.386369i) q^{14} +(3.72739 - 1.05194i) q^{15} +(3.54924 - 2.57867i) q^{16} +(0.182555 + 0.251266i) q^{17} +(0.232725 + 4.46093i) q^{18} +(-5.72886 - 1.86142i) q^{19} +(-0.470524 + 0.119646i) q^{20} +(-1.15396 + 0.885250i) q^{21} +(-4.92832 + 0.316183i) q^{22} -5.74665 q^{23} +(0.119818 + 4.59653i) q^{24} +(-4.95761 - 0.649699i) q^{25} +(3.44794 - 1.12031i) q^{26} +(-4.42948 - 2.71656i) q^{27} +(0.147498 - 0.107163i) q^{28} +(0.755560 + 2.32538i) q^{29} +(1.99506 - 5.41078i) q^{30} +(-2.24512 - 1.63117i) q^{31} -1.22298i q^{32} +(2.94456 - 4.93250i) q^{33} +0.462456 q^{34} +(1.81972 - 0.462723i) q^{35} +(0.546194 + 0.354887i) q^{36} +(8.50603 - 2.76378i) q^{37} +(-7.25629 + 5.27200i) q^{38} +(-1.19822 + 4.04335i) q^{39} +(2.19804 - 5.51416i) q^{40} +(-2.71666 + 8.36103i) q^{41} +(0.0564319 + 2.16488i) q^{42} -3.32121 q^{43} +(-0.385101 + 0.608485i) q^{44} +(3.87193 + 5.47797i) q^{45} +(-5.02954 + 6.92257i) q^{46} +(-0.122317 + 0.376453i) q^{47} +(6.26176 + 4.30468i) q^{48} +(5.09268 - 3.70005i) q^{49} +(-5.12161 + 5.40344i) q^{50} +(-0.304747 + 0.443297i) q^{51} +(0.163359 - 0.502768i) q^{52} +(6.06755 + 4.40833i) q^{53} +(-7.14918 + 2.95830i) q^{54} +(-6.00456 + 4.35262i) q^{55} +2.22916i q^{56} +(-0.271873 - 10.4298i) q^{57} +(3.46248 + 1.12503i) q^{58} +(10.5430 - 3.42562i) q^{59} +(-0.467306 - 0.699105i) q^{60} +(-4.35961 - 6.00049i) q^{61} +(-3.92991 + 1.27691i) q^{62} +(-2.11237 - 1.37251i) q^{63} +(5.62525 + 4.08698i) q^{64} +(3.48008 - 4.18686i) q^{65} +(-3.36471 - 7.86408i) q^{66} -1.70411i q^{67} +(0.0396366 - 0.0545551i) q^{68} +(-3.32143 - 9.38297i) q^{69} +(1.03523 - 2.59707i) q^{70} +(0.389936 + 0.536701i) q^{71} +(-7.43583 + 2.85232i) q^{72} +(4.98888 + 15.3542i) q^{73} +(4.11526 - 12.6655i) q^{74} +(-1.80457 - 8.47015i) q^{75} +1.30787i q^{76} +(1.48936 - 2.35328i) q^{77} +(3.82203 + 4.98220i) q^{78} +(1.31923 - 1.81576i) q^{79} +(-5.23713 - 8.29492i) q^{80} +(1.87539 - 8.80244i) q^{81} +(7.69425 + 10.5902i) q^{82} +(0.260754 + 0.358897i) q^{83} +(0.260223 + 0.178892i) q^{84} +(0.587233 - 0.370759i) q^{85} +(-2.90677 + 4.00082i) q^{86} +(-3.36011 + 2.57767i) q^{87} +(-3.25134 - 8.18236i) q^{88} -16.7081i q^{89} +(9.98767 + 0.130166i) q^{90} +(-0.631782 + 1.94442i) q^{91} +(0.385566 + 1.18665i) q^{92} +(1.36571 - 4.60855i) q^{93} +(0.346431 + 0.476822i) q^{94} +(-4.98748 + 12.5120i) q^{95} +(1.99684 - 0.706853i) q^{96} +(1.67704 - 2.30824i) q^{97} -9.37311i q^{98} +(9.75554 + 1.95692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9}+O(q^{10}) $ 80 * q + 4 * q^4 - 10 * q^6 - 10 * q^9	$ 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} - 2 q^{15} - 60 q^{16} - 20 q^{19} - 30 q^{24} + 6 q^{25} + 10 q^{30} - 20 q^{31} - 56 q^{34} + 2 q^{36} - 50 q^{39} + 60 q^{40} - 92 q^{45} - 40 q^{46} + 72 q^{49} + 30 q^{51} + 4 q^{55} + 54 q^{60} + 96 q^{64} - 42 q^{66} + 30 q^{69} - 86 q^{70} + 2 q^{75} - 66 q^{81} + 140 q^{84} - 30 q^{85} + 120 q^{90} + 48 q^{91} + 60 q^{94} - 70 q^{96} + 60 q^{99}+O(q^{100}) $ 80 * q + 4 * q^4 - 10 * q^6 - 10 * q^9 - 2 * q^15 - 60 * q^16 - 20 * q^19 - 30 * q^24 + 6 * q^25 + 10 * q^30 - 20 * q^31 - 56 * q^34 + 2 * q^36 - 50 * q^39 + 60 * q^40 - 92 * q^45 - 40 * q^46 + 72 * q^49 + 30 * q^51 + 4 * q^55 + 54 * q^60 + 96 * q^64 - 42 * q^66 + 30 * q^69 - 86 * q^70 + 2 * q^75 - 66 * q^81 + 140 * q^84 - 30 * q^85 + 120 * q^90 + 48 * q^91 + 60 * q^94 - 70 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

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 $

$2$	0.875212	−	1.20463i	0.618869	−	0.851799i	−0.378401	−	0.925642i	$-0.623526\pi$
$2$	0.875212	−	1.20463i	0.618869	−	0.851799i	0.997270	+	0.0738422i	$0.0235261\pi$
$3$	0.577976	+	1.63277i	0.333695	+	0.942681i
$3$	0.577976	+	1.63277i	0.333695	+	0.942681i
$4$	−0.0670941	−	0.206494i	−0.0335470	−	0.103247i
$5$	0.145586	−	2.23132i	0.0651081	−	0.997878i
$5$	0.145586	−	2.23132i	0.0651081	−	0.997878i
$6$	2.47273	+	0.732776i	1.00949	+	0.299155i
$7$	0.259482	+	0.798604i	0.0980751	+	0.301844i	0.988043	−	0.154179i	$-0.0492733\pi$
$7$	0.259482	+	0.798604i	0.0980751	+	0.301844i	−0.889968	+	0.456023i	$0.849273\pi$
$8$	2.52478	+	0.820350i	0.892643	+	0.290037i
$9$	−2.33189	+	1.88741i	−0.777296	+	0.629136i
$10$	−2.56049	−	2.12826i	−0.809699	−	0.673014i
$11$	−2.11726	−	2.55289i	−0.638376	−	0.769724i
$11$	−2.11726	−	2.55289i	−0.638376	−	0.769724i
$12$	0.298379	−	0.228898i	0.0861347	−	0.0660772i
$13$	1.96978	+	1.43113i	0.546318	+	0.396923i	0.826426	−	0.563045i	$-0.190370\pi$
$13$	1.96978	+	1.43113i	0.546318	+	0.396923i	−0.280108	+	0.959968i	$0.590370\pi$
$14$	1.18912	+	0.386369i	0.317806	+	0.103261i
$15$	3.72739	−	1.05194i	0.962407	−	0.271611i
$16$	3.54924	−	2.57867i	0.887310	−	0.644668i
$17$	0.182555	+	0.251266i	0.0442762	+	0.0609410i	0.830581	−	0.556898i	$-0.188008\pi$
$17$	0.182555	+	0.251266i	0.0442762	+	0.0609410i	−0.786305	+	0.617839i	$0.788008\pi$
$18$	0.232725	+	4.46093i	0.0548537	+	1.05145i
$19$	−5.72886	−	1.86142i	−1.31429	−	0.427039i	−0.433761	−	0.901028i	$-0.642814\pi$
$19$	−5.72886	−	1.86142i	−1.31429	−	0.427039i	−0.880531	+	0.473989i	$0.842814\pi$
$20$	−0.470524	+	0.119646i	−0.105212	+	0.0267536i
$21$	−1.15396	+	0.885250i	−0.251816	+	0.193177i
$22$	−4.92832	+	0.316183i	−1.05072	+	0.0674105i
$23$	−5.74665			−1.19826			−0.599130	−	0.800652i	$-0.704487\pi$
$23$	−5.74665			−1.19826			−0.599130	+	0.800652i	$0.704487\pi$
$24$	0.119818	+	4.59653i	0.0244577	+	0.938262i
$25$	−4.95761	−	0.649699i	−0.991522	−	0.129940i
$26$	3.44794	−	1.12031i	0.676198	−	0.219710i
$27$	−4.42948	−	2.71656i	−0.852454	−	0.522802i
$28$	0.147498	−	0.107163i	0.0278744	−	0.0202519i
$29$	0.755560	+	2.32538i	0.140304	+	0.431811i	0.996377	−	0.0850431i	$-0.0271028\pi$
$29$	0.755560	+	2.32538i	0.140304	+	0.431811i	−0.856073	+	0.516855i	$0.827103\pi$
$30$	1.99506	−	5.41078i	0.364246	−	0.987869i
$31$	−2.24512	−	1.63117i	−0.403235	−	0.292968i	0.367622	−	0.929975i	$-0.380172\pi$
$31$	−2.24512	−	1.63117i	−0.403235	−	0.292968i	−0.770857	+	0.637008i	$0.780172\pi$
$32$		−	1.22298i		−	0.216194i
$33$	2.94456	−	4.93250i	0.512582	−	0.858638i
$34$	0.462456			0.0793106
$35$	1.81972	−	0.462723i	0.307589	−	0.0782145i
$36$	0.546194	+	0.354887i	0.0910324	+	0.0591479i
$37$	8.50603	−	2.76378i	1.39838	−	0.454362i	0.489715	−	0.871883i	$-0.337101\pi$
$37$	8.50603	−	2.76378i	1.39838	−	0.454362i	0.908667	+	0.417521i	$0.137101\pi$
$38$	−7.25629	+	5.27200i	−1.17713	+	0.855232i
$39$	−1.19822	+	4.04335i	−0.191868	+	0.647454i
$40$	2.19804	−	5.51416i	0.347540	−	0.871865i
$41$	−2.71666	+	8.36103i	−0.424271	+	1.30577i	0.479419	+	0.877586i	$0.340847\pi$
$41$	−2.71666	+	8.36103i	−0.424271	+	1.30577i	−0.903690	+	0.428187i	$0.859153\pi$
$42$	0.0564319	+	2.16488i	0.00870763	+	0.334048i
$43$	−3.32121			−0.506480			−0.253240	−	0.967403i	$-0.581496\pi$
$43$	−3.32121			−0.506480			−0.253240	+	0.967403i	$0.581496\pi$
$44$	−0.385101	+	0.608485i	−0.0580562	+	0.0917325i
$45$	3.87193	+	5.47797i	0.577193	+	0.816608i
$46$	−5.02954	+	6.92257i	−0.741565	+	1.02068i
$47$	−0.122317	+	0.376453i	−0.0178417	+	0.0549113i	−0.959581	−	0.281433i	$-0.909190\pi$
$47$	−0.122317	+	0.376453i	−0.0178417	+	0.0549113i	0.941739	+	0.336344i	$0.109190\pi$
$48$	6.26176	+	4.30468i	0.903807	+	0.621328i
$49$	5.09268	−	3.70005i	0.727526	−	0.528578i
$50$	−5.12161	+	5.40344i	−0.724304	+	0.764162i
$51$	−0.304747	+	0.443297i	−0.0426732	+	0.0620740i
$52$	0.163359	−	0.502768i	0.0226538	−	0.0697213i
$53$	6.06755	+	4.40833i	0.833442	+	0.605531i	0.920531	−	0.390669i	$-0.127756\pi$
$53$	6.06755	+	4.40833i	0.833442	+	0.605531i	−0.0870888	+	0.996201i	$0.527756\pi$
$54$	−7.14918	+	2.95830i	−0.972880	+	0.402574i
$55$	−6.00456	+	4.35262i	−0.809655	+	0.586907i
$56$			2.22916i			0.297885i
$57$	−0.271873	−	10.4298i	−0.0360105	−	1.38146i
$58$	3.46248	+	1.12503i	0.454646	+	0.147724i
$59$	10.5430	−	3.42562i	1.37258	−	0.445978i	0.472357	−	0.881407i	$-0.343403\pi$
$59$	10.5430	−	3.42562i	1.37258	−	0.445978i	0.900223	+	0.435429i	$0.143403\pi$
$60$	−0.467306	−	0.699105i	−0.0603289	−	0.0902541i
$61$	−4.35961	−	6.00049i	−0.558191	−	0.768284i	0.432904	−	0.901440i	$-0.357489\pi$
$61$	−4.35961	−	6.00049i	−0.558191	−	0.768284i	−0.991095	+	0.133156i	$0.957489\pi$
$62$	−3.92991	+	1.27691i	−0.499099	+	0.162167i
$63$	−2.11237	−	1.37251i	−0.266134	−	0.172920i
$64$	5.62525	+	4.08698i	0.703156	+	0.510872i
$65$	3.48008	−	4.18686i	0.431650	−	0.519316i
$66$	−3.36471	−	7.86408i	−0.414167	−	0.968001i
$67$		−	1.70411i		−	0.208190i	−0.994567	−	0.104095i	$-0.966805\pi$
$67$		−	1.70411i		−	0.208190i	0.994567	−	0.104095i	$-0.0331947\pi$
$68$	0.0396366	−	0.0545551i	0.00480665	−	0.00661578i
$69$	−3.32143	−	9.38297i	−0.399853	−	1.12958i
$70$	1.03523	−	2.59707i	0.123734	−	0.310409i
$71$	0.389936	+	0.536701i	0.0462769	+	0.0636947i	0.831528	−	0.555482i	$-0.187466\pi$
$71$	0.389936	+	0.536701i	0.0462769	+	0.0636947i	−0.785251	+	0.619177i	$0.787466\pi$
$72$	−7.43583	+	2.85232i	−0.876320	+	0.336149i
$73$	4.98888	+	15.3542i	0.583905	+	1.79707i	0.603625	+	0.797269i	$0.293723\pi$
$73$	4.98888	+	15.3542i	0.583905	+	1.79707i	−0.0197201	+	0.999806i	$0.506277\pi$
$74$	4.11526	−	12.6655i	0.478390	−	1.47233i
$75$	−1.80457	−	8.47015i	−0.208374	−	0.978049i
$76$			1.30787i			0.150023i
$77$	1.48936	−	2.35328i	0.169728	−	0.268181i
$78$	3.82203	+	4.98220i	0.432760	+	0.564123i
$79$	1.31923	−	1.81576i	0.148425	−	0.204289i	−0.728330	−	0.685226i	$-0.759703\pi$
$79$	1.31923	−	1.81576i	0.148425	−	0.204289i	0.876755	+	0.480937i	$0.159703\pi$
$80$	−5.23713	−	8.29492i	−0.585529	−	0.927400i
$81$	1.87539	−	8.80244i	0.208377	−	0.978049i
$82$	7.69425	+	10.5902i	0.849688	+	1.16950i
$83$	0.260754	+	0.358897i	0.0286214	+	0.0393940i	0.823088	−	0.567914i	$-0.192249\pi$
$83$	0.260754	+	0.358897i	0.0286214	+	0.0393940i	−0.794466	+	0.607308i	$0.792249\pi$
$84$	0.260223	+	0.178892i	0.0283927	+	0.0195187i
$85$	0.587233	−	0.370759i	0.0636944	−	0.0402145i
$86$	−2.90677	+	4.00082i	−0.313445	+	0.431420i
$87$	−3.36011	+	2.57767i	−0.360242	+	0.276355i
$88$	−3.25134	−	8.18236i	−0.346594	−	0.872242i
$89$		−	16.7081i		−	1.77105i	−0.464588	−	0.885527i	$-0.653798\pi$
$89$		−	16.7081i		−	1.77105i	0.464588	−	0.885527i	$-0.346202\pi$
$90$	9.98767	+	0.130166i	1.05279	+	0.0137207i
$91$	−0.631782	+	1.94442i	−0.0662287	+	0.203831i
$92$	0.385566	+	1.18665i	0.0401981	+	0.123717i
$93$	1.36571	−	4.60855i	0.141617	−	0.477884i
$94$	0.346431	+	0.476822i	0.0357317	+	0.0491804i
$95$	−4.98748	+	12.5120i	−0.511704	+	1.28370i
$96$	1.99684	−	0.706853i	0.203802	−	0.0721429i
$97$	1.67704	−	2.30824i	0.170277	−	0.234366i	−0.715347	−	0.698770i	$-0.753731\pi$
$97$	1.67704	−	2.30824i	0.170277	−	0.234366i	0.885624	+	0.464403i	$0.153731\pi$
$98$		−	9.37311i		−	0.946827i
$99$	9.75554	+	1.95692i	0.980468	+	0.196678i
$100$	0.198467	+	1.06731i	0.0198467	+	0.106731i
$101$	−11.6689	−	8.47798i	−1.16110	−	0.843591i	−0.171186	−	0.985239i	$-0.554760\pi$
$101$	−11.6689	−	8.47798i	−1.16110	−	0.843591i	−0.989917	+	0.141648i	$0.954760\pi$
$102$	0.267289	+	0.755086i	0.0264655	+	0.0747646i
$103$	−4.42164	+	1.43668i	−0.435677	+	0.141560i	−0.518640	−	0.854993i	$-0.673562\pi$
$103$	−4.42164	+	1.43668i	−0.435677	+	0.141560i	0.0829633	+	0.996553i	$0.473562\pi$
$104$	3.79922	+	5.22918i	0.372544	+	0.512763i
$105$	1.80728	+	2.70375i	0.176372	+	0.263859i
$106$	10.6208	−	3.45090i	1.03158	−	0.335181i
$107$	15.7841	+	5.12856i	1.52591	+	0.495797i	0.947447	−	0.319914i	$-0.103654\pi$
$107$	15.7841	+	5.12856i	1.52591	+	0.495797i	0.578460	+	0.815711i	$0.303654\pi$
$108$	−0.263763	+	1.09693i	−0.0253806	+	0.105552i
$109$			17.4265i			1.66915i	0.550893	+	0.834576i	$0.314287\pi$
$109$			17.4265i			1.66915i	−0.550893	+	0.834576i	$0.685713\pi$
$110$	−0.0119874	+	11.0427i	−0.00114295	+	1.05288i
$111$	9.42890	+	12.2910i	0.894952	+	1.16661i
$112$	2.98030	+	2.16532i	0.281612	+	0.204603i
$113$	0.0373195	−	0.114858i	0.00351073	−	0.0108049i	−0.949286	−	0.314414i	$-0.898192\pi$
$113$	0.0373195	−	0.114858i	0.00351073	−	0.0108049i	0.952797	+	0.303610i	$0.0981918\pi$
$114$	−12.8019	−	8.80077i	−1.19901	−	0.824268i
$115$	−0.836633	+	12.8226i	−0.0780164	+	1.19572i
$116$	0.429483	−	0.312038i	0.0398765	−	0.0289720i
$117$	−7.29441	+	0.380546i	−0.674369	+	0.0351815i
$118$	5.10076	−	15.6985i	0.469563	−	1.44517i
$119$	−0.153292	+	0.210989i	−0.0140523	+	0.0193413i
$120$	10.2738	+	0.401838i	0.937864	+	0.0366826i
$121$	−2.03446	+	10.8102i	−0.184951	+	0.982748i
$122$	−11.0439			−0.999871
$123$	−15.2218	+	0.396787i	−1.37250	+	0.0357771i
$124$	−0.186194	+	0.573046i	−0.0167207	+	0.0514611i
$125$	−2.17145	+	10.9674i	−0.194220	+	0.980958i
$126$	−3.50213	+	1.34339i	−0.311995	+	0.119679i
$127$	4.49454	−	3.26548i	0.398826	−	0.289764i	−0.370237	−	0.928937i	$-0.620723\pi$
$127$	4.49454	−	3.26548i	0.398826	−	0.289764i	0.769063	+	0.639173i	$0.220723\pi$
$128$	12.1728	−	3.95519i	1.07593	−	0.349592i
$129$	−1.91958	−	5.42278i	−0.169010	−	0.477450i
$130$	−1.99779	−	7.85658i	−0.175218	−	0.689068i
$131$	−2.08974			−0.182582			−0.0912908	−	0.995824i	$-0.529099\pi$
$131$	−2.08974			−0.182582			−0.0912908	+	0.995824i	$0.529099\pi$
$132$	−1.21610	−	0.277093i	−0.105848	−	0.0241178i
$133$		−	5.05810i		−	0.438593i
$134$	−2.05282	−	1.49146i	−0.177336	−	0.128842i
$135$	−6.70640	+	9.48811i	−0.577195	+	0.816606i
$136$	0.254786	+	0.784150i	0.0218477	+	0.0672403i
$137$	8.15234	−	5.92302i	0.696502	−	0.506038i	−0.182289	−	0.983245i	$-0.558351\pi$
$137$	8.15234	−	5.92302i	0.696502	−	0.506038i	0.878791	+	0.477207i	$0.158351\pi$
$138$	−14.2099	−	4.21101i	−1.20963	−	0.358465i
$139$	0.794812	−	0.258250i	0.0674151	−	0.0219045i	−0.275115	−	0.961411i	$-0.588716\pi$
$139$	0.794812	−	0.258250i	0.0674151	−	0.0219045i	0.342530	+	0.939507i	$0.388716\pi$
$140$	−0.217642	−	0.344716i	−0.0183941	−	0.0291338i
$141$	−0.685357	+	0.0178652i	−0.0577175	+	0.00150452i
$142$	0.987801			0.0828944
$143$	−0.517016	−	8.05867i	−0.0432350	−	0.673900i
$144$	−3.40942	+	12.7120i	−0.284118	+	1.05934i
$145$	5.29866	−	1.34736i	0.440030	−	0.111892i
$146$	22.8624	+	7.42845i	1.89211	+	0.614783i
$147$	8.98479	+	6.17664i	0.741053	+	0.509441i
$148$	−1.14141	−	1.57101i	−0.0938232	−	0.129136i
$149$	−2.06392	+	1.49953i	−0.169083	+	0.122846i	−0.669109	−	0.743165i	$-0.733324\pi$
$149$	−2.06392	+	1.49953i	−0.169083	+	0.122846i	0.500026	+	0.866011i	$0.333324\pi$
$150$	−11.7828	−	5.23935i	−0.962058	−	0.427791i
$151$	6.96223	+	2.26217i	0.566578	+	0.184092i	0.578279	−	0.815839i	$-0.303725\pi$
$151$	6.96223	+	2.26217i	0.566578	+	0.184092i	−0.0117006	+	0.999932i	$0.503725\pi$
$152$	−12.9371	−	9.39934i	−1.04934	−	0.762387i
$153$	−0.899940	−	0.241367i	−0.0727558	−	0.0195134i
$154$	−1.53132	−	3.85374i	−0.123397	−	0.310543i
$155$	−3.96654	+	4.77211i	−0.318600	+	0.383305i
$156$	0.915322	−	0.0238597i	0.0732844	−	0.00191031i
$157$	−5.49526	−	1.78552i	−0.438570	−	0.142500i	0.0814060	−	0.996681i	$-0.474059\pi$
$157$	−5.49526	−	1.78552i	−0.438570	−	0.142500i	−0.519976	+	0.854181i	$0.674059\pi$
$158$	−1.03271	−	3.17835i	−0.0821580	−	0.252856i
$159$	−3.69090	+	12.4548i	−0.292708	+	0.987733i
$160$	−2.72886	−	0.178049i	−0.215735	−	0.0140760i
$161$	−1.49115	−	4.58930i	−0.117519	−	0.361688i
$162$	−8.96228	−	9.96314i	−0.704144	−	0.782779i
$163$	−8.84432	+	12.1732i	−0.692741	+	0.953476i	0.307258	+	0.951626i	$0.400589\pi$
$163$	−8.84432	+	12.1732i	−0.692741	+	0.953476i	−0.999998	+	0.00184945i	$0.999411\pi$
$164$	1.90878			0.149050
$165$	−10.5773	−	7.28836i	−0.823443	−	0.567398i
$166$	0.660551			0.0512687
$167$	−10.7740	+	14.8292i	−0.833718	+	1.14751i	0.153501	+	0.988148i	$0.450945\pi$
$167$	−10.7740	+	14.8292i	−0.833718	+	1.14751i	−0.987220	+	0.159366i	$0.949055\pi$
$168$	−3.63972	+	1.28840i	−0.280810	+	0.0994025i
$169$	−2.18532	−	6.72574i	−0.168102	−	0.517364i
$170$	0.0673272	−	1.03189i	0.00516376	−	0.0791423i
$171$	16.8723	−	6.47208i	1.29026	−	0.494932i
$172$	0.222834	+	0.685812i	0.0169909	+	0.0522927i
$173$	−4.64092	−	1.50793i	−0.352843	−	0.114646i	0.127232	−	0.991873i	$-0.459391\pi$
$173$	−4.64092	−	1.50793i	−0.352843	−	0.114646i	−0.480075	+	0.877227i	$0.659391\pi$
$174$	0.164318	+	6.30369i	0.0124569	+	0.477881i
$175$	−0.767559	−	4.12775i	−0.0580220	−	0.312029i
$176$	−14.0977	−	3.60110i	−1.06265	−	0.271443i
$177$	11.6869	+	15.2344i	0.878438	+	1.14508i
$178$	−20.1270	−	14.6231i	−1.50858	−	1.09605i
$179$	13.7067	+	4.45358i	1.02449	+	0.332876i	0.772608	−	0.634883i	$-0.218952\pi$
$179$	13.7067	+	4.45358i	1.02449	+	0.332876i	0.251878	+	0.967759i	$0.418952\pi$
$180$	0.871387	−	1.16707i	0.0649493	−	0.0869883i
$181$	−10.9139	+	7.92938i	−0.811220	+	0.589386i	−0.914184	−	0.405299i	$-0.867167\pi$
$181$	−10.9139	+	7.92938i	−0.811220	+	0.589386i	0.102964	+	0.994685i	$0.467167\pi$
$182$	1.78936	+	2.46284i	0.132636	+	0.182558i
$183$	7.27768	−	10.5864i	0.537981	−	0.782569i
$184$	−14.5090	−	4.71426i	−1.06962	−	0.347540i
$185$	−4.92852	−	19.3821i	−0.362352	−	1.42500i
$186$	−4.35629	−	5.67863i	−0.319419	−	0.416377i
$187$	0.254937	−	0.998038i	0.0186429	−	0.0729837i
$188$	0.0859420			0.00626797
$189$	1.02009	−	4.24230i	0.0742004	−	0.308582i
$190$	10.7071	+	16.9587i	0.776777	+	1.23031i
$191$	−4.72843	+	1.53636i	−0.342137	+	0.111167i	−0.475045	−	0.879961i	$-0.657568\pi$
$191$	−4.72843	+	1.53636i	−0.342137	+	0.111167i	0.132908	+	0.991128i	$0.457568\pi$
$192$	−3.42185	+	11.5469i	−0.246950	+	0.833327i
$193$	10.7665	−	7.82230i	0.774988	−	0.563062i	−0.128483	−	0.991712i	$-0.541011\pi$
$193$	10.7665	−	7.82230i	0.774988	−	0.563062i	0.903471	+	0.428650i	$0.141011\pi$
$194$	−1.31281	−	4.04040i	−0.0942540	−	0.290084i
$195$	8.84758	+	3.26227i	0.633589	+	0.233616i
$196$	−1.10573	−	0.803358i	−0.0789805	−	0.0573827i
$197$			0.0885134i			0.00630632i	0.999995	+	0.00315316i	$0.00100368\pi$
$197$			0.0885134i			0.00630632i	−0.999995	+	0.00315316i	$0.998996\pi$
$198$	10.8955	−	10.0391i	0.774311	−	0.713444i
$199$	−25.7489			−1.82529			−0.912645	−	0.408753i	$-0.865964\pi$
$199$	−25.7489			−1.82529			−0.912645	+	0.408753i	$0.865964\pi$
$200$	−11.9839	−	5.70732i	−0.847388	−	0.403568i
$201$	2.78242	−	0.984936i	0.196257	−	0.0694720i
$202$	−20.4256	+	6.63668i	−1.43714	+	0.466955i
$203$	−1.66100	+	1.20679i	−0.116579	+	0.0846999i
$204$	0.111985	+	0.0331860i	0.00784052	+	0.00232348i
$205$	18.2606	+	7.27900i	1.27538	+	0.508387i
$206$	−2.13921	+	6.58382i	−0.149046	+	0.458716i
$207$	13.4005	−	10.8463i	0.931402	−	0.753868i
$208$	10.6816			0.740637
$209$	7.37747	+	18.5662i	0.510310	+	1.28425i
$210$	4.83876	+	0.189258i	0.333906	+	0.0130601i
$211$	13.8532	−	19.0672i	0.953691	−	1.31264i	0.00382262	−	0.999993i	$-0.498783\pi$
$211$	13.8532	−	19.0672i	0.953691	−	1.31264i	0.949868	−	0.312650i	$-0.101217\pi$
$212$	0.503199	−	1.54869i	0.0345599	−	0.106364i
$213$	−0.650936	+	0.946877i	−0.0446014	+	0.0648789i
$214$	19.9924	−	14.5254i	1.36666	−	0.992933i
$215$	−0.483523	+	7.41070i	−0.0329760	+	0.505406i
$216$	−8.95492	−	10.4924i	−0.609305	−	0.713920i
$217$	0.720094	−	2.21622i	0.0488832	−	0.150447i
$218$	20.9924	+	15.2518i	1.42178	+	1.03299i
$219$	−22.1865	+	17.0201i	−1.49922	+	1.15011i
$220$	1.30166	+	0.947872i	0.0877579	+	0.0639055i
$221$			0.756198i			0.0508674i
$222$	23.0584	−	0.601062i	1.54758	−	0.0403407i
$223$	−19.2109	−	6.24199i	−1.28646	−	0.417995i	−0.415606	−	0.909545i	$-0.636430\pi$
$223$	−19.2109	−	6.24199i	−1.28646	−	0.417995i	−0.870849	+	0.491550i	$0.836430\pi$
$224$	0.976676	−	0.317341i	0.0652569	−	0.0212033i
$225$	12.7868	−	7.84200i	0.852455	−	0.522800i
$226$	−0.105698	−	0.145481i	−0.00703093	−	0.00967725i
$227$	0.613801	−	0.199436i	0.0407394	−	0.0132370i	−0.288576	−	0.957457i	$-0.593182\pi$
$227$	0.613801	−	0.199436i	0.0407394	−	0.0132370i	0.329316	+	0.944220i	$0.393182\pi$
$228$	−2.13545	+	0.755917i	−0.141424	+	0.0500618i
$229$	14.9958	+	10.8951i	0.990949	+	0.719966i	0.960129	−	0.279559i	$-0.0901881\pi$
$229$	14.9958	+	10.8951i	0.990949	+	0.719966i	0.0308200	+	0.999525i	$0.490188\pi$
$230$	14.7143	+	12.2304i	0.970230	+	0.806446i
$231$	4.70318	+	1.07164i	0.309446	+	0.0705087i
$232$			6.49088i			0.426147i
$233$	−8.11799	+	11.1735i	−0.531827	+	0.731998i	−0.987408	−	0.158197i	$-0.949432\pi$
$233$	−8.11799	+	11.1735i	−0.531827	+	0.731998i	0.455580	+	0.890195i	$0.349432\pi$
$234$	−5.92574	+	9.12010i	−0.387378	+	0.596200i
$235$	0.822180	+	0.327735i	0.0536331	+	0.0213791i
$236$	−1.41474	−	1.94723i	−0.0920920	−	0.126754i
$237$	3.72721	+	1.10453i	0.242108	+	0.0717470i
$238$	0.119999	+	0.369320i	0.00777840	+	0.0239394i
$239$	−2.85846	+	8.79745i	−0.184899	+	0.569059i	−0.999947	−	0.0103340i	$-0.996711\pi$
$239$	−2.85846	+	8.79745i	−0.184899	+	0.569059i	0.815048	+	0.579393i	$0.196711\pi$
$240$	10.5168	−	13.3453i	0.678854	−	0.861436i
$241$		−	10.2810i		−	0.662260i	−0.943585	−	0.331130i	$-0.892570\pi$
$241$		−	10.2810i		−	0.662260i	0.943585	−	0.331130i	$-0.107430\pi$
$242$	11.2417	+	11.9120i	0.722644	+	0.765733i
$243$	15.4563	−	2.02552i	0.991522	−	0.129937i
$244$	−0.946563	+	1.30283i	−0.0605975	+	0.0834053i
$245$	−7.51458	−	11.9021i	−0.480089	−	0.760397i
$246$	−12.8443	+	18.6839i	−0.818925	+	1.19124i
$247$	−8.62065	−	11.8653i	−0.548519	−	0.754972i
$248$	−4.33029	−	5.96013i	−0.274974	−	0.378469i
$249$	−0.435287	+	0.633185i	−0.0275852	+	0.0401265i
$250$	11.3112	+	12.2146i	0.715383	+	0.772521i
$251$	1.70243	−	2.34320i	0.107456	−	0.147901i	−0.751902	−	0.659275i	$-0.770863\pi$
$251$	1.70243	−	2.34320i	0.107456	−	0.147901i	0.859358	+	0.511374i	$0.170863\pi$
$252$	−0.141687	+	0.528280i	−0.00892543	+	0.0332785i
$253$	12.1671	+	14.6706i	0.764941	+	0.922330i
$254$		−	8.27223i		−	0.519046i
$255$	0.944773	+	0.744528i	0.0591640	+	0.0466241i
$256$	1.59197	−	4.89957i	0.0994979	−	0.306223i
$257$	−3.03436	−	9.33880i	−0.189278	−	0.582538i	0.810718	−	0.585437i	$-0.199077\pi$
$257$	−3.03436	−	9.33880i	−0.189278	−	0.582538i	−0.999996	+	0.00289901i	$0.999077\pi$
$258$	−8.21247	−	2.43371i	−0.511286	−	0.151516i
$259$	4.41433	+	6.07580i	0.274293	+	0.377532i
$260$	−1.09805	−	0.437703i	−0.0680984	−	0.0271452i
$261$	−6.15081	−	3.99646i	−0.380726	−	0.247375i
$262$	−1.82897	+	2.51736i	−0.112994	+	0.155523i
$263$		−	26.6343i		−	1.64234i	−0.570681	−	0.821172i	$-0.693321\pi$
$263$		−	26.6343i		−	1.64234i	0.570681	−	0.821172i	$-0.306679\pi$
$264$	11.4807	−	10.0379i	0.706590	−	0.617790i
$265$	10.7198	−	12.8969i	0.658510	−	0.792249i
$266$	−6.09312	−	4.42691i	−0.373593	−	0.271431i
$267$	27.2805	−	9.65688i	1.66954	−	0.590992i
$268$	−0.351889	+	0.114336i	−0.0214951	+	0.00698417i
$269$	0.0552221	+	0.0760067i	0.00336695	+	0.00463421i	0.810697	−	0.585466i	$-0.199088\pi$
$269$	0.0552221	+	0.0760067i	0.00336695	+	0.00463421i	−0.807330	+	0.590100i	$0.799088\pi$
$270$	5.56010	+	16.3828i	0.338377	+	0.997026i
$271$	−15.6499	+	5.08497i	−0.950666	+	0.308890i	−0.742986	−	0.669307i	$-0.766591\pi$
$271$	−15.6499	+	5.08497i	−0.950666	+	0.308890i	−0.207680	+	0.978197i	$0.566591\pi$
$272$	1.29587	+	0.421052i	0.0785734	+	0.0255300i
$273$	−3.53995	+	0.0922760i	−0.214248	+	0.00558480i
$274$		−	15.0044i		−	0.906451i
$275$	8.83792	+	14.0318i	0.532946	+	0.846149i
$276$	−1.71468	+	1.31540i	−0.103212	+	0.0791777i
$277$	1.04104	+	0.756358i	0.0625498	+	0.0454451i	0.618621	−	0.785690i	$-0.287692\pi$
$277$	1.04104	+	0.756358i	0.0625498	+	0.0454451i	−0.556071	+	0.831135i	$0.687692\pi$
$278$	0.384534	−	1.18347i	0.0230628	−	0.0709801i
$279$	8.31405	−	0.433740i	0.497749	−	0.0259673i
$280$	4.97399	+	0.324535i	0.297252	+	0.0193947i
$281$	9.81270	−	7.12934i	0.585376	−	0.425301i	−0.255282	−	0.966867i	$-0.582168\pi$
$281$	9.81270	−	7.12934i	0.585376	−	0.425301i	0.840658	+	0.541566i	$0.182168\pi$
$282$	−0.578312	+	0.841235i	−0.0344380	+	0.0500948i
$283$	−6.04941	+	18.6182i	−0.359600	+	1.10673i	0.593694	+	0.804691i	$0.297669\pi$
$283$	−6.04941	+	18.6182i	−0.359600	+	1.10673i	−0.953294	+	0.302044i	$0.902331\pi$
$284$	0.0846633	−	0.116529i	0.00502384	−	0.00691472i
$285$	−23.3118	−	0.911794i	−1.38087	−	0.0540100i
$286$	−10.1602	−	6.43024i	−0.600785	−	0.380228i
$287$	−7.38208			−0.435750
$288$	2.30826	+	2.85185i	0.136015	+	0.168047i
$289$	5.22348	−	16.0762i	0.307264	−	0.945660i
$290$	3.01439	−	7.56213i	0.177011	−	0.444064i
$291$	4.73812	+	1.40411i	0.277753	+	0.0823102i
$292$	2.83583	−	2.06035i	0.165954	−	0.120573i
$293$	8.83686	−	2.87127i	0.516255	−	0.167741i	−0.0392900	−	0.999228i	$-0.512510\pi$
$293$	8.83686	−	2.87127i	0.516255	−	0.167741i	0.555545	+	0.831486i	$0.312510\pi$
$294$	15.3041	−	5.41743i	0.892556	−	0.315951i
$295$	−6.10877	−	24.0235i	−0.355666	−	1.39870i
$296$	23.7431			1.38004
$297$	2.44327	+	17.0596i	0.141773	+	0.989899i
$298$			3.79866i			0.220051i
$299$	−11.3196	−	8.22419i	−0.654631	−	0.475617i
$300$	−1.62796	+	0.940931i	−0.0939905	+	0.0543247i
$301$	−0.861796	−	2.65234i	−0.0496731	−	0.152878i
$302$	8.81850	−	6.40701i	0.507447	−	0.368682i
$303$	7.09824	−	23.9528i	0.407783	−	1.37605i
$304$	−25.1331	+	8.16624i	−1.44148	+	0.468366i
$305$	−14.0237	+	8.85412i	−0.802997	+	0.506985i
$306$	−1.07840	+	0.872844i	−0.0616478	+	0.0498971i
$307$	−23.0974			−1.31824			−0.659118	−	0.752039i	$-0.729070\pi$
$307$	−23.0974			−1.31824			−0.659118	+	0.752039i	$0.729070\pi$
$308$	−0.585865	−	0.149653i	−0.0333828	−	0.00852725i
$309$	−4.90137	−	6.38916i	−0.278829	−	0.363467i
$310$	2.27705	+	8.95480i	0.129328	+	0.508599i
$311$	−14.6627	−	4.76420i	−0.831445	−	0.270153i	−0.137791	−	0.990461i	$-0.544000\pi$
$311$	−14.6627	−	4.76420i	−0.831445	−	0.270153i	−0.693654	+	0.720309i	$0.744000\pi$
$312$	−6.34219	+	9.22560i	−0.359056	+	0.522297i
$313$	−11.3737	−	15.6546i	−0.642880	−	0.884848i	0.355886	−	0.934530i	$-0.384179\pi$
$313$	−11.3737	−	15.6546i	−0.642880	−	0.884848i	−0.998765	+	0.0496818i	$0.984179\pi$
$314$	−6.96040	+	5.05703i	−0.392798	+	0.285385i
$315$	−3.37004	+	4.51357i	−0.189880	+	0.254311i
$316$	−0.463457	−	0.150586i	−0.0260715	−	0.00847114i
$317$	−9.38868	−	6.82127i	−0.527321	−	0.383121i	0.292034	−	0.956408i	$-0.405668\pi$
$317$	−9.38868	−	6.82127i	−0.527321	−	0.383121i	−0.819355	+	0.573287i	$0.805668\pi$
$318$	11.7731	+	15.3468i	0.660203	+	0.860605i
$319$	4.33671	−	6.85227i	0.242809	−	0.383654i
$320$	9.93833	−	11.9567i	0.555570	−	0.668402i
$321$	0.749062	+	28.7360i	0.0418086	+	1.60389i
$322$	−6.83347	−	2.22033i	−0.380814	−	0.123734i
$323$	−0.578124	−	1.77928i	−0.0321677	−	0.0990019i
$324$	−1.94348	+	0.203334i	−0.107971	+	0.0112963i
$325$	−8.83558	−	8.37473i	−0.490110	−	0.464546i
$326$	6.92346	+	21.3082i	0.383455	+	1.18015i
$327$	−28.4534	+	10.0721i	−1.57348	+	0.556987i
$328$	−13.7179	+	18.8811i	−0.757446	+	1.04253i
$329$	−0.332376			−0.0183245
$330$	−18.0372	+	6.36286i	−0.992913	+	0.350264i
$331$	4.08935			0.224771			0.112385	−	0.993665i	$-0.464151\pi$
$331$	4.08935			0.224771			0.112385	+	0.993665i	$0.464151\pi$
$332$	0.0566151	−	0.0779240i	0.00310716	−	0.00427663i
$333$	−14.6187	+	22.4992i	−0.801101	+	1.23295i
$334$	8.43405	+	25.9573i	0.461490	+	1.42032i
$335$	−3.80242	−	0.248095i	−0.207749	−	0.0135549i
$336$	−1.81292	+	6.11766i	−0.0989031	+	0.333746i
$337$	−5.91989	−	18.2196i	−0.322477	−	0.992482i	−0.972567	−	0.232625i	$-0.925269\pi$
$337$	−5.91989	−	18.2196i	−0.322477	−	0.992482i	0.650089	−	0.759858i	$-0.274731\pi$
$338$	−10.0146	−	3.25395i	−0.544724	−	0.176991i
$339$	0.209106	−	0.00545077i	0.0113571	−	0.000296045i
$340$	−0.115960	−	0.0963846i	−0.00628879	−	0.00522719i
$341$	0.589286	+	9.18515i	0.0319116	+	0.497404i
$342$	6.97043	−	25.9893i	0.376918	−	1.40534i
$343$	9.03167	+	6.56189i	0.487664	+	0.354309i
$344$	−8.38532	−	2.72456i	−0.452106	−	0.146898i
$345$	−21.4200	+	6.04516i	−1.15321	+	0.325460i
$346$	−5.87828	+	4.27082i	−0.316018	+	0.229601i
$347$	6.87069	+	9.45670i	0.368838	+	0.507662i	0.952585	−	0.304274i	$-0.0984138\pi$
$347$	6.87069	+	9.45670i	0.368838	+	0.507662i	−0.583747	+	0.811936i	$0.698414\pi$
$348$	0.757718	+	0.520897i	0.0406179	+	0.0279230i
$349$	8.60838	+	2.79703i	0.460796	+	0.149722i	0.530210	−	0.847866i	$-0.322113\pi$
$349$	8.60838	+	2.79703i	0.460796	+	0.149722i	−0.0694142	+	0.997588i	$0.522113\pi$
$350$	−5.64418	−	2.68804i	−0.301694	−	0.143682i
$351$	−4.83734	−	11.6902i	−0.258198	−	0.623975i
$352$	−3.12213	+	2.58936i	−0.166410	+	0.138013i
$353$	−9.10247			−0.484476			−0.242238	−	0.970217i	$-0.577881\pi$
$353$	−9.10247			−0.484476			−0.242238	+	0.970217i	$0.577881\pi$
$354$	28.5802	−	0.745000i	1.51902	−	0.0395963i
$355$	1.25432	−	0.791937i	0.0665725	−	0.0420317i
$356$	−3.45012	+	1.12101i	−0.182856	+	0.0594136i
$357$	−0.433096	−	0.128345i	−0.0229219	−	0.00679272i
$358$	17.3612	−	12.6136i	0.917566	−	0.666651i
$359$	−1.38757	−	4.27051i	−0.0732334	−	0.225389i	0.907739	−	0.419534i	$-0.137807\pi$
$359$	−1.38757	−	4.27051i	−0.0732334	−	0.225389i	−0.980973	+	0.194145i	$0.937807\pi$
$360$	5.28189	+	17.0070i	0.278380	+	0.896347i
$361$	13.9837	+	10.1597i	0.735983	+	0.534723i
$362$			20.0870i			1.05575i
$363$	−18.8265	+	2.92624i	−0.988135	+	0.153588i
$364$	0.443901			0.0232667
$365$	34.9865	−	8.89646i	1.83128	−	0.465662i
$366$	−6.38313	−	18.0322i	−0.333652	−	0.942559i
$367$	8.72302	−	2.83428i	0.455338	−	0.147948i	−0.0723634	−	0.997378i	$-0.523054\pi$
$367$	8.72302	−	2.83428i	0.455338	−	0.147948i	0.527701	+	0.849430i	$0.323054\pi$
$368$	−20.3962	+	14.8187i	−1.06323	+	0.772480i
$369$	−9.44571	−	24.6244i	−0.491724	−	1.28190i
$370$	−27.6617	−	11.0264i	−1.43806	−	0.573235i
$371$	−1.94609	+	5.98946i	−0.101036	+	0.310957i
$372$	−1.04327	+	0.0271949i	−0.0540910	+	0.00140999i
$373$	31.6743			1.64003			0.820016	−	0.572340i	$-0.193964\pi$
$373$	31.6743			1.64003			0.820016	+	0.572340i	$0.193964\pi$
$374$	−0.979138	−	1.18060i	−0.0506300	−	0.0610473i
$375$	−19.1624	+	2.79344i	−0.989541	+	0.144253i
$376$	−0.617645	+	0.850116i	−0.0318526	+	0.0438414i
$377$	−1.83962	+	5.66177i	−0.0947453	+	0.291596i
$378$	−4.21760	−	4.94174i	−0.216930	−	0.254176i
$379$	7.52965	−	5.47061i	0.386772	−	0.281006i	−0.377359	−	0.926067i	$-0.623168\pi$
$379$	7.52965	−	5.47061i	0.386772	−	0.281006i	0.764131	+	0.645061i	$0.223168\pi$
$380$	2.91828	+	0.190407i	0.149704	+	0.00976769i
$381$	7.92951	+	5.45119i	0.406241	+	0.279273i
$382$	−2.28764	+	7.04063i	−0.117046	+	0.360230i
$383$	21.7551	+	15.8060i	1.11164	+	0.807651i	0.982920	−	0.184031i	$-0.0589146\pi$
$383$	21.7551	+	15.8060i	1.11164	+	0.807651i	0.128715	+	0.991682i	$0.458915\pi$
$384$	13.4935	+	17.5894i	0.688588	+	0.897606i
$385$	−5.03410	−	3.66584i	−0.256561	−	0.186829i
$386$		−	19.8158i		−	1.00860i
$387$	7.74470	−	6.26848i	0.393685	−	0.318645i
$388$	−0.589158	−	0.191429i	−0.0299100	−	0.00971833i
$389$	−10.8590	+	3.52831i	−0.550575	+	0.178893i	−0.571076	−	0.820897i	$-0.693474\pi$
$389$	−10.8590	+	3.52831i	−0.550575	+	0.178893i	0.0205011	+	0.999790i	$0.493474\pi$
$390$	11.6733	−	7.80285i	0.591102	−	0.395113i
$391$	−1.04908	−	1.44394i	−0.0530544	−	0.0730231i
$392$	15.8932	−	5.16402i	0.802729	−	0.260822i
$393$	−1.20782	−	3.41207i	−0.0609265	−	0.172116i
$394$	0.106626	+	0.0774680i	0.00537172	+	0.00390278i
$395$	−3.85949	−	3.20797i	−0.194192	−	0.161411i
$396$	−0.250446	−	2.14576i	−0.0125854	−	0.107828i
$397$		−	13.2971i		−	0.667363i	−0.942686	−	0.333681i	$-0.891709\pi$
$397$		−	13.2971i		−	0.667363i	0.942686	−	0.333681i	$-0.108291\pi$
$398$	−22.5357	+	31.0178i	−1.12961	+	1.55478i
$399$	8.25873	−	2.92346i	0.413453	−	0.146356i
$400$	−19.2711	+	10.4781i	−0.963555	+	0.523906i
$401$	−12.7867	−	17.5994i	−0.638538	−	0.878872i	0.359999	−	0.932953i	$-0.382777\pi$
$401$	−12.7867	−	17.5994i	−0.638538	−	0.878872i	−0.998537	+	0.0540808i	$0.982777\pi$
$402$	1.24873	−	4.21381i	0.0622811	−	0.210166i
$403$	−2.08797	−	6.42610i	−0.104009	−	0.320107i
$404$	−0.967738	+	2.97839i	−0.0481468	+	0.148181i
$405$	−19.3681	−	5.46611i	−0.962406	−	0.271613i
$406$			3.05708i			0.151720i
$407$	−25.0650	−	15.8633i	−1.24243	−	0.786315i
$408$	−1.13308	+	0.869227i	−0.0560957	+	0.0430331i
$409$	−11.1044	+	15.2839i	−0.549078	+	0.755740i	−0.989887	−	0.141860i	$-0.954692\pi$
$409$	−11.1044	+	15.2839i	−0.549078	+	0.755740i	0.440809	+	0.897601i	$0.354692\pi$
$410$	24.7504	−	15.6266i	1.22234	−	0.771742i
$411$	14.3828	+	9.88755i	0.709452	+	0.487717i
$412$	0.593331	+	0.816651i	0.0292313	+	0.0402335i
$413$	5.47144	+	7.53079i	0.269232	+	0.370566i
$414$	−1.33739	−	25.6354i	−0.0657290	−	1.25991i
$415$	0.838777	−	0.529576i	0.0411739	−	0.0259958i
$416$	1.75024	−	2.40899i	0.0858124	−	0.118111i
$417$	0.881046	+	1.14848i	0.0431450	+	0.0562415i
$418$	28.8222	+	7.36231i	1.40974	+	0.360102i
$419$		−	22.2396i		−	1.08648i	−0.839579	−	0.543238i	$-0.817198\pi$
$419$		−	22.2396i		−	1.08648i	0.839579	−	0.543238i	$-0.182802\pi$
$420$	0.437051	−	0.554598i	0.0213259	−	0.0270616i
$421$	−5.65642	+	17.4087i	−0.275677	+	0.848446i	0.713363	+	0.700795i	$0.247171\pi$
$421$	−5.65642	+	17.4087i	−0.275677	+	0.848446i	−0.989039	+	0.147651i	$0.952829\pi$
$422$	−10.8444	−	33.3758i	−0.527899	−	1.62471i
$423$	−0.425290	−	1.10871i	−0.0206783	−	0.0539071i
$424$	11.7028	+	16.1076i	0.568340	+	0.782253i
$425$	−0.741791	−	1.36429i	−0.0359822	−	0.0661775i
$426$	0.570925	+	1.61285i	0.0276614	+	0.0781430i
$427$	3.66078	−	5.03863i	0.177157	−	0.243836i
$428$		−	3.60342i		−	0.174178i
$429$	12.8592	−	5.50189i	0.620846	−	0.265634i
$430$	8.50394	+	7.06840i	0.410097	+	0.340869i
$431$	18.6351	+	13.5392i	0.897623	+	0.652161i	0.937854	−	0.347029i	$-0.112810\pi$
$431$	18.6351	+	13.5392i	0.897623	+	0.652161i	−0.0402314	+	0.999190i	$0.512810\pi$
$432$	−22.7264	+	1.78046i	−1.09342	+	0.0856622i
$433$	22.8557	−	7.42627i	1.09837	−	0.356884i	0.296898	−	0.954909i	$-0.404048\pi$
$433$	22.8557	−	7.42627i	1.09837	−	0.356884i	0.801477	+	0.598026i	$0.204048\pi$
$434$	−2.03948	−	2.80711i	−0.0978984	−	0.134746i
$435$	5.26243	+	7.87277i	0.252314	+	0.377470i
$436$	3.59846	−	1.16921i	0.172335	−	0.0559951i
$437$	32.9218	+	10.6969i	1.57486	+	0.511704i
$438$	1.08498	+	41.6226i	0.0518422	+	1.98880i
$439$		−	22.8635i		−	1.09121i	−0.838041	−	0.545607i	$-0.816299\pi$
$439$		−	22.8635i		−	1.09121i	0.838041	−	0.545607i	$-0.183701\pi$
$440$	−18.7308	+	6.06355i	−0.892958	+	0.289068i
$441$	−4.89206	+	18.2401i	−0.232955	+	0.868574i
$442$	0.910936	+	0.661834i	0.0433288	+	0.0314802i
$443$	−2.61128	+	8.03669i	−0.124066	+	0.381835i	−0.993730	−	0.111809i	$-0.964335\pi$
$443$	−2.61128	+	8.03669i	−0.124066	+	0.381835i	0.869664	+	0.493644i	$0.164335\pi$
$444$	1.90540	−	2.77167i	0.0904262	−	0.131538i
$445$	−37.2812	−	2.43246i	−1.76730	−	0.115310i
$446$	−24.3329	+	17.6789i	−1.15219	+	0.837118i
$447$	−3.64129	−	2.50322i	−0.172227	−	0.118398i
$448$	−1.80423	+	5.55284i	−0.0852418	+	0.262347i
$449$	−12.3658	+	17.0201i	−0.583581	+	0.803230i	−0.994082	−	0.108630i	$-0.965354\pi$
$449$	−12.3658	+	17.0201i	−0.583581	+	0.803230i	0.410502	+	0.911860i	$0.365354\pi$
$450$	1.74451	−	22.2668i	0.0822369	−	1.04967i
$451$	27.0966	−	10.7671i	1.27593	−	0.507003i
$452$	−0.0262214			−0.00123335
$453$	0.330405	+	12.6752i	0.0155238	+	0.595533i
$454$	0.296960	−	0.913950i	0.0139370	−	0.0428938i
$455$	4.24666	+	1.69279i	0.199086	+	0.0793592i
$456$	7.86965	−	26.5559i	0.368530	−	1.24359i
$457$	−23.4701	+	17.0520i	−1.09789	+	0.797660i	−0.980713	−	0.195451i	$-0.937383\pi$
$457$	−23.4701	+	17.0520i	−1.09789	+	0.797660i	−0.117172	+	0.993112i	$0.537383\pi$
$458$	26.2490	−	8.52881i	1.22653	−	0.398525i
$459$	−0.126046	−	1.60890i	−0.00588333	−	0.0750971i
$460$	2.70394	−	0.687563i	0.126072	−	0.0320578i
$461$	16.9353			0.788757			0.394378	−	0.918948i	$-0.370960\pi$
$461$	16.9353			0.788757			0.394378	+	0.918948i	$0.370960\pi$
$462$	5.40720	−	4.72766i	0.251566	−	0.219951i
$463$			11.4918i			0.534068i	0.963687	+	0.267034i	$0.0860437\pi$
$463$			11.4918i			0.534068i	−0.963687	+	0.267034i	$0.913956\pi$
$464$	8.67805	+	6.30497i	0.402868	+	0.292701i
$465$	−10.0843	−	3.71828i	−0.467650	−	0.172431i
$466$	6.35488	+	19.5583i	0.294384	+	0.906021i
$467$	25.5366	−	18.5534i	1.18169	−	0.858550i	0.189331	−	0.981913i	$-0.439368\pi$
$467$	25.5366	−	18.5534i	1.18169	−	0.858550i	0.992362	+	0.123363i	$0.0393680\pi$
$468$	0.567992	+	1.48072i	0.0262554	+	0.0684464i
$469$	1.36091	−	0.442187i	0.0628410	−	0.0204183i
$470$	1.11438	−	0.703582i	0.0514025	−	0.0324538i
$471$	−0.260787	−	10.0045i	−0.0120164	−	0.460983i
$472$	29.4289			1.35457
$473$	7.03186	+	8.47868i	0.323325	+	0.389850i
$474$	4.59264	−	3.52319i	0.210947	−	0.161826i
$475$	27.1921	+	12.9502i	1.24766	+	0.594198i
$476$	0.0538530	+	0.0174979i	0.00246835	+	0.000802014i
$477$	−22.4692	+	1.17220i	−1.02879	+	0.0536716i
$478$	8.09587	+	11.1430i	0.370297	+	0.509670i
$479$	−6.97638	+	5.06864i	−0.318759	+	0.231592i	−0.735646	−	0.677366i	$-0.763121\pi$
$479$	−6.97638	+	5.06864i	−0.318759	+	0.231592i	0.416887	+	0.908958i	$0.363121\pi$
$480$	−1.28650	−	4.55851i	−0.0587206	−	0.208067i
$481$	20.7103	+	6.72918i	0.944308	+	0.306824i
$482$	−12.3848	−	8.99810i	−0.564113	−	0.409852i
$483$	6.63143	−	5.08722i	0.301741	−	0.231477i
$484$	2.36875	−	0.305197i	0.107670	−	0.0138726i
$485$	−4.90628	−	4.07806i	−0.222783	−	0.185175i
$486$	11.0876	−	20.3918i	0.502942	−	0.924992i
$487$	34.7245	+	11.2827i	1.57352	+	0.511266i	0.960376	−	0.278708i	$-0.0899061\pi$
$487$	34.7245	+	11.2827i	1.57352	+	0.511266i	0.613140	+	0.789974i	$0.289906\pi$
$488$	−6.08454	−	18.7263i	−0.275434	−	0.847700i
$489$	−24.9878	−	7.40496i	−1.12999	−	0.334864i
$490$	−20.9144	−	1.36459i	−0.944818	−	0.0616461i
$491$	−11.5791	−	35.6367i	−0.522556	−	1.60826i	−0.769099	−	0.639129i	$-0.779295\pi$
$491$	−11.5791	−	35.6367i	−0.522556	−	1.60826i	0.246543	−	0.969132i	$-0.420705\pi$
$492$	1.10323	+	3.11659i	0.0497373	+	0.140507i
$493$	−0.446356	+	0.614357i	−0.0201029	+	0.0276692i
$494$	−21.8382			−0.982546
$495$	5.78679	−	21.4829i	0.260097	−	0.965583i
$496$	−12.1747			−0.546661
$497$	−0.327430	+	0.450669i	−0.0146872	+	0.0202153i
$498$	0.381783	+	1.07853i	0.0171081	+	0.0483301i
$499$	0.669241	+	2.05971i	0.0299593	+	0.0922054i	0.964918	−	0.262551i	$-0.0845638\pi$
$499$	0.669241	+	2.05971i	0.0299593	+	0.0922054i	−0.934959	+	0.354756i	$0.884564\pi$
$500$	2.41041	−	0.287459i	0.107797	−	0.0128555i
$501$	−30.4398	−	9.02060i	−1.35995	−	0.403011i
$502$	−1.33269	−	4.10159i	−0.0594807	−	0.183063i
$503$	−27.3239	−	8.87809i	−1.21831	−	0.395854i	−0.371847	−	0.928294i	$-0.621275\pi$
$503$	−27.3239	−	8.87809i	−1.21831	−	0.395854i	−0.846468	+	0.532440i	$0.821275\pi$
$504$	−4.20734	−	5.19816i	−0.187410	−	0.231544i
$505$	−20.6160	+	24.8029i	−0.917398	+	1.10371i
$506$	28.3214	−	1.81700i	1.25904	−	0.0807754i
$507$	9.71853	−	7.45545i	0.431615	−	0.331108i
$508$	−0.975859	−	0.709003i	−0.0432967	−	0.0314569i
$509$	19.0581	+	6.19235i	0.844736	+	0.274471i	0.699239	−	0.714888i	$-0.253522\pi$
$509$	19.0581	+	6.19235i	0.844736	+	0.274471i	0.145496	+	0.989359i	$0.453522\pi$
$510$	1.72375	−	0.486478i	0.0763291	−	0.0215416i
$511$	−10.9674	+	7.96829i	−0.485170	+	0.352496i
$512$	10.5376	+	14.5037i	0.465700	+	0.640981i
$513$	20.3192	+	23.8079i	0.897116	+	1.05115i
$514$	−13.9055	−	4.51816i	−0.613344	−	0.199288i
$515$	2.56196	+	10.0753i	0.112894	+	0.443969i
$516$	−0.990981	+	0.760220i	−0.0436255	+	0.0334668i
$517$	1.22002	−	0.484785i	0.0536563	−	0.0213208i
$518$	11.1825			0.491333
$519$	−0.220243	−	8.44911i	−0.00966760	−	0.370875i
$520$	12.2211	−	7.71599i	0.535931	−	0.338369i
$521$	14.8418	−	4.82239i	0.650231	−	0.211273i	0.0347148	−	0.999397i	$-0.488948\pi$
$521$	14.8418	−	4.82239i	0.650231	−	0.211273i	0.615516	+	0.788125i	$0.288948\pi$
$522$	−10.1975	+	3.91168i	−0.446333	+	0.171209i
$523$	−18.0675	+	13.1268i	−0.790037	+	0.573995i	−0.907974	−	0.419026i	$-0.862372\pi$
$523$	−18.0675	+	13.1268i	−0.790037	+	0.573995i	0.117938	+	0.993021i	$0.462372\pi$
$524$	0.140209	+	0.431520i	0.00612507	+	0.0188510i
$525$	6.29605	−	3.63899i	0.274782	−	0.158819i
$526$	−32.0844	−	23.3107i	−1.39895	−	1.01639i
$527$		−	0.861902i		−	0.0375450i
$528$	−2.26837	−	25.0997i	−0.0987182	−	1.09232i
$529$	10.0240			0.435827
$530$	−6.15384	−	24.2008i	−0.267306	−	1.05122i
$531$	−18.1195	+	27.8871i	−0.786320	+	1.21020i
$532$	−1.04447	+	0.339369i	−0.0452835	+	0.0147135i
$533$	−17.3169	+	12.5815i	−0.750078	+	0.544964i
$534$	12.2433	−	41.3146i	0.529819	−	1.78786i
$535$	13.7414	−	34.4728i	0.594094	−	1.49039i
$536$	1.39797	−	4.30250i	0.0603830	−	0.185840i
$537$	0.650475	+	24.9540i	0.0280701	+	1.07684i
$538$	0.139891			0.00603112
$539$	−20.2283	−	5.16709i	−0.871295	−	0.222562i
$540$	2.40920	+	0.748237i	0.103675	+	0.0321990i
$541$	−4.61175	+	6.34754i	−0.198275	+	0.272902i	−0.896564	−	0.442914i	$-0.853945\pi$
$541$	−4.61175	+	6.34754i	−0.198275	+	0.272902i	0.698289	+	0.715815i	$0.253945\pi$
$542$	−7.57152	+	23.3028i	−0.325225	+	1.00094i
$543$	−19.2548	−	13.2368i	−0.826303	−	0.568047i
$544$	0.307293	−	0.223261i	0.0131751	−	0.00957225i
$545$	38.8841	+	2.53705i	1.66561	+	0.108675i
$546$	−2.98705	+	4.34508i	−0.127834	+	0.185952i
$547$	−9.75347	+	30.0181i	−0.417028	+	1.28348i	0.493396	+	0.869805i	$0.335755\pi$
$547$	−9.75347	+	30.0181i	−0.417028	+	1.28348i	−0.910424	+	0.413676i	$0.864245\pi$
$548$	−1.77004	−	1.28601i	−0.0756126	−	0.0549357i
$549$	21.4915	+	5.76410i	0.917234	+	0.246006i
$550$	24.6381	+	1.63441i	1.05057	+	0.0696916i
$551$		−	14.7282i		−	0.627442i
$552$	−0.688551	−	26.4146i	−0.0293067	−	1.12428i
$553$	1.79239	+	0.582383i	0.0762202	+	0.0247655i
$554$	1.82226	−	0.592087i	0.0774203	−	0.0251554i
$555$	28.7979	−	19.2495i	1.22240	−	0.817097i
$556$	−0.106654	−	0.146797i	−0.00452315	−	0.00622558i
$557$	−37.1728	+	12.0782i	−1.57506	+	0.511769i	−0.960779	−	0.277316i	$-0.910555\pi$
$557$	−37.1728	+	12.0782i	−1.57506	+	0.511769i	−0.614284	+	0.789085i	$0.710555\pi$
$558$	6.75407	−	10.3949i	0.285922	−	0.440053i
$559$	−6.54205	−	4.75308i	−0.276699	−	0.201034i
$560$	5.26541	−	6.33478i	0.222504	−	0.267693i
$561$	1.77692	−	0.160588i	0.0750214	−	0.00678003i
$562$		−	18.0603i		−	0.761829i
$563$	5.84141	−	8.04001i	0.246186	−	0.338846i	−0.667985	−	0.744175i	$-0.732843\pi$
$563$	5.84141	−	8.04001i	0.246186	−	0.338846i	0.914171	+	0.405329i	$0.132843\pi$
$564$	0.0496725	+	0.140324i	0.00209159	+	0.00590869i
$565$	−0.250852	−	0.0999936i	−0.0105534	−	0.00420676i
$566$	17.1334	+	23.5821i	0.720171	+	0.991230i
$567$	7.51630	−	0.786383i	0.315655	−	0.0330250i
$568$	0.544219	+	1.67493i	0.0228349	+	0.0702786i
$569$	−11.6643	+	35.8991i	−0.488994	+	1.50497i	0.337119	+	0.941462i	$0.390548\pi$
$569$	−11.6643	+	35.8991i	−0.488994	+	1.50497i	−0.826112	+	0.563506i	$0.809452\pi$
$570$	−21.5012	+	27.2840i	−0.900584	+	1.14280i
$571$			19.5186i			0.816829i	0.912797	+	0.408414i	$0.133918\pi$
$571$			19.5186i			0.816829i	−0.912797	+	0.408414i	$0.866082\pi$
$572$	−1.62938	+	0.647450i	−0.0681279	+	0.0270712i
$573$	−5.24144	−	6.83246i	−0.218964	−	0.285430i
$574$	−6.46088	+	8.89264i	−0.269672	+	0.371172i
$575$	28.4897	+	3.73360i	1.18810	+	0.155702i
$576$	−20.8312	+	1.08675i	−0.867968	+	0.0452814i
$577$	0.640516	+	0.881595i	0.0266650	+	0.0367013i	0.822141	−	0.569283i	$-0.192779\pi$
$577$	0.640516	+	0.881595i	0.0266650	+	0.0367013i	−0.795476	+	0.605985i	$0.792779\pi$
$578$	−14.7942	−	20.3624i	−0.615357	−	0.846966i
$579$	18.9948	+	13.0581i	0.789397	+	0.542676i
$580$	−0.633730	−	1.00374i	−0.0263142	−	0.0416782i
$581$	−0.218956	+	0.301366i	−0.00908381	+	0.0125028i
$582$	5.83828	−	4.47877i	0.242005	−	0.185651i
$583$	−1.59258	−	24.8233i	−0.0659578	−	1.02808i
$584$			42.8586i			1.77350i
$585$	−0.212844	+	16.3316i	−0.00880003	+	0.675228i
$586$	4.27532	−	13.1581i	0.176612	−	0.543556i
$587$	3.49714	+	10.7631i	0.144342	+	0.444240i	0.996926	−	0.0783509i	$-0.0249655\pi$
$587$	3.49714	+	10.7631i	0.144342	+	0.444240i	−0.852583	+	0.522591i	$0.824965\pi$
$588$	0.672616	−	2.26972i	0.0277382	−	0.0936018i
$589$	9.82568	+	13.5239i	0.404860	+	0.557242i
$590$	−34.2859	−	13.6669i	−1.41153	−	0.562658i
$591$	−0.144522	+	0.0511587i	−0.00594485	+	0.00210439i
$592$	23.0631	−	31.7436i	0.947886	−	1.30465i
$593$			11.8491i			0.486583i	0.969953	+	0.243292i	$0.0782272\pi$
$593$			11.8491i			0.486583i	−0.969953	+	0.243292i	$0.921773\pi$
$594$	22.6888	+	11.9876i	0.930934	+	0.491856i
$595$	0.448467	+	0.372762i	0.0183853	+	0.0152817i
$596$	0.448121	+	0.325579i	0.0183558	+	0.0133362i
$597$	−14.8822	−	42.0421i	−0.609090	−	1.72067i
$598$	−19.8141	+	6.43800i	−0.810261	+	0.263270i
$599$	−1.06761	−	1.46944i	−0.0436214	−	0.0600397i	0.786649	−	0.617400i	$-0.211814\pi$
$599$	−1.06761	−	1.46944i	−0.0436214	−	0.0600397i	−0.830271	+	0.557361i	$0.811814\pi$
$600$	2.39235	−	22.8656i	0.0976673	−	0.933485i
$601$	−1.91562	+	0.622424i	−0.0781399	+	0.0253892i	−0.347826	−	0.937559i	$-0.613080\pi$
$601$	−1.91562	+	0.622424i	−0.0781399	+	0.0253892i	0.269686	+	0.962948i	$0.413080\pi$
$602$	−3.94933	−	1.28321i	−0.160963	−	0.0522999i
$603$	3.21635	+	3.97379i	0.130980	+	0.161825i
$604$		−	1.58944i		−	0.0646734i
$605$	23.8249	+	6.11336i	0.968621	+	0.248543i
$606$	−22.6417	−	29.5145i	−0.919756	−	1.19894i
$607$	19.2387	+	13.9777i	0.780874	+	0.567338i	0.905241	−	0.424898i	$-0.139690\pi$
$607$	19.2387	+	13.9777i	0.780874	+	0.567338i	−0.124367	+	0.992236i	$0.539690\pi$
$608$	−2.27648	+	7.00628i	−0.0923234	+	0.284142i
$609$	−2.93043	−	2.01454i	−0.118747	−	0.0816333i
$610$	−1.60784	+	24.6426i	−0.0650997	+	0.997749i
$611$	−0.779688	+	0.566476i	−0.0315428	+	0.0229172i
$612$	0.0105396	+	0.202027i	0.000426039	+	0.00816645i
$613$	6.14878	−	18.9240i	0.248347	−	0.764333i	−0.746721	−	0.665137i	$-0.768373\pi$
$613$	6.14878	−	18.9240i	0.248347	−	0.764333i	0.995068	−	0.0991959i	$-0.0316271\pi$
$614$	−20.2151	+	27.8237i	−0.815815	+	1.12287i
$615$	−1.33072	+	34.0226i	−0.0536599	+	1.37192i
$616$	5.69080	−	4.71971i	0.229289	−	0.190162i
$617$	−7.42907			−0.299083			−0.149542	−	0.988755i	$-0.547780\pi$
$617$	−7.42907			−0.299083			−0.149542	+	0.988755i	$0.547780\pi$
$618$	−11.9863	+	0.312447i	−0.482159	+	0.0125685i
$619$	−3.02156	+	9.29941i	−0.121447	+	0.373775i	−0.993237	−	0.116105i	$-0.962959\pi$
$619$	−3.02156	+	9.29941i	−0.121447	+	0.373775i	0.871790	+	0.489879i	$0.162959\pi$
$620$	1.25154	+	0.498887i	0.0502632	+	0.0200358i
$621$	25.4547	+	15.6111i	1.02146	+	0.626453i
$622$	−18.5720	+	13.4934i	−0.744671	+	0.541035i
$623$	13.3432	−	4.33545i	0.534582	−	0.173696i
$624$	6.17372	+	17.4406i	0.247147	+	0.698184i
$625$	24.1558	+	6.44191i	0.966231	+	0.257676i
$626$	−28.8123			−1.15157
$627$	−26.0504	+	22.7766i	−1.04035	+	0.909609i
$628$			1.25454i			0.0500615i
$629$	2.24727	+	1.63273i	0.0896043	+	0.0651014i
$630$	2.48767	+	8.00997i	0.0991112	+	0.319125i
$631$	−11.8841	−	36.5754i	−0.473098	−	1.45604i	−0.848506	−	0.529185i	$-0.822498\pi$
$631$	−11.8841	−	36.5754i	−0.473098	−	1.45604i	0.375409	−	0.926859i	$-0.377502\pi$
$632$	4.82031	−	3.50216i	0.191742	−	0.139309i
$633$	39.1392	+	11.5986i	1.55565	+	0.461004i
$634$	−16.4342	+	5.33978i	−0.652684	+	0.212070i
$635$	−6.63199	−	10.5042i	−0.263182	−	0.416846i
$636$	2.81949	−	0.0734957i	0.111800	−	0.00291429i
$637$	15.3267			0.607265
$638$	−4.45889	−	11.2213i	−0.176529	−	0.444256i
$639$	−1.92226	−	0.515557i	−0.0760434	−	0.0203951i
$640$	−7.05311	−	27.7373i	−0.278799	−	1.09641i
$641$	−35.1825	−	11.4315i	−1.38962	−	0.451516i	−0.483804	−	0.875177i	$-0.660745\pi$
$641$	−35.1825	−	11.4315i	−1.38962	−	0.451516i	−0.905821	+	0.423660i	$0.860745\pi$
$642$	35.2718	+	24.2478i	1.39207	+	0.956983i
$643$	−11.1695	−	15.3735i	−0.440482	−	0.606271i	0.529837	−	0.848099i	$-0.322253\pi$
$643$	−11.1695	−	15.3735i	−0.440482	−	0.606271i	−0.970319	+	0.241828i	$0.922253\pi$
$644$	−0.847617	+	0.615830i	−0.0334008	+	0.0242671i
$645$	−12.3795	+	3.49373i	−0.487440	+	0.137565i
$646$	−2.64935	−	0.860826i	−0.104237	−	0.0338688i
$647$	3.08779	+	2.24341i	0.121394	+	0.0881975i	0.646825	−	0.762638i	$-0.276096\pi$
$647$	3.08779	+	2.24341i	0.121394	+	0.0881975i	−0.525432	+	0.850836i	$0.676096\pi$
$648$	11.9560	−	20.6857i	0.469677	−	0.812612i
$649$	−31.0674	−	19.6621i	−1.21950	−	0.771806i
$650$	−17.8214	+	3.31391i	−0.699014	+	0.129982i
$651$	4.03478	−	0.105175i	0.158136	−	0.00412212i
$652$	3.10709	+	1.00955i	0.121683	+	0.0395372i
$653$	9.63447	+	29.6518i	0.377026	+	1.16037i	0.942102	+	0.335327i	$0.108847\pi$
$653$	9.63447	+	29.6518i	0.377026	+	1.16037i	−0.565076	+	0.825039i	$0.691153\pi$
$654$	−12.7697	+	43.0909i	−0.499334	+	1.68499i
$655$	−0.304237	+	4.66289i	−0.0118875	+	0.182194i
$656$	11.9183	+	36.6807i	0.465330	+	1.43214i
$657$	−40.6132	−	26.3882i	−1.58447	−	1.02950i
$658$	−0.290899	+	0.400389i	−0.0113404	+	0.0156088i
$659$	25.0775			0.976880			0.488440	−	0.872598i	$-0.337566\pi$
$659$	25.0775			0.976880			0.488440	+	0.872598i	$0.337566\pi$
$660$	−0.795330	+	2.67316i	−0.0309582	+	0.104053i
$661$	15.8866			0.617918			0.308959	−	0.951075i	$-0.400019\pi$
$661$	15.8866			0.617918			0.308959	+	0.951075i	$0.400019\pi$
$662$	3.57905	−	4.92614i	0.139104	−	0.191460i
$663$	−1.23470	+	0.437064i	−0.0479517	+	0.0169742i
$664$	0.363924	+	1.12004i	0.0141230	+	0.0434661i
$665$	−11.2863	−	0.736389i	−0.437663	−	0.0285559i
$666$	14.3086	+	37.3016i	0.554446	+	1.44541i
$667$	−4.34194	−	13.3631i	−0.168121	−	0.517422i
$668$	3.78501	+	1.22982i	0.146446	+	0.0475833i
$669$	−0.911686	−	34.9747i	−0.0352478	−	1.35220i
$670$	−3.62679	+	4.36336i	−0.140115	+	0.168571i
$671$	−6.08816	+	23.8342i	−0.235031	+	0.920108i
$672$	1.08264	+	1.41127i	0.0417638	+	0.0544410i
$673$	−24.0483	−	17.4721i	−0.926995	−	0.673501i	0.0182602	−	0.999833i	$-0.494187\pi$
$673$	−24.0483	−	17.4721i	−0.926995	−	0.673501i	−0.945255	+	0.326332i	$0.894187\pi$
$674$	−27.1289	−	8.81472i	−1.04497	−	0.339530i
$675$	20.1947	+	16.3455i	0.777294	+	0.629138i
$676$	−1.24220	+	0.902514i	−0.0477771	+	0.0347121i
$677$	−16.0277	−	22.0602i	−0.615995	−	0.847844i	0.381059	−	0.924551i	$-0.375559\pi$
$677$	−16.0277	−	22.0602i	−0.615995	−	0.847844i	−0.997054	+	0.0767069i	$0.975559\pi$
$678$	0.176446	−	0.256665i	0.00677638	−	0.00985718i
$679$	2.27853	+	0.740340i	0.0874421	+	0.0284116i
$680$	1.78679	−	0.454348i	0.0685201	−	0.0174235i
$681$	0.680396	+	0.886928i	0.0260728	+	0.0339872i
$682$	11.5804	+	7.32908i	0.443437	+	0.280645i
$683$	15.5577			0.595300			0.297650	−	0.954675i	$-0.403797\pi$
$683$	15.5577			0.595300			0.297650	+	0.954675i	$0.403797\pi$
$684$	−2.46848	−	3.04980i	−0.0943847	−	0.116612i
$685$	−12.0293	−	19.0528i	−0.459617	−	0.727971i
$686$	15.8093	−	5.13674i	0.603600	−	0.196122i
$687$	−9.12195	+	30.7818i	−0.348024	+	1.17440i
$688$	−11.7878	+	8.56433i	−0.449405	+	0.326512i
$689$	5.64284	+	17.3669i	0.214975	+	0.661625i
$690$	−11.4649	+	31.0939i	−0.436461	+	1.18372i
$691$	−14.9402	−	10.8547i	−0.568353	−	0.412933i	0.266153	−	0.963931i	$-0.414247\pi$
$691$	−14.9402	−	10.8547i	−0.568353	−	0.412933i	−0.834507	+	0.550998i	$0.814247\pi$
$692$			1.05950i			0.0402760i
$693$	0.968584	+	8.29860i	0.0367935	+	0.315238i
$694$	17.4051			0.660688
$695$	−0.460526	−	1.81108i	−0.0174687	−	0.0686982i
$696$	−10.5981	+	3.75157i	−0.401721	+	0.142203i
$697$	−2.59678	+	0.843746i	−0.0983602	+	0.0319592i
$698$	10.9035	−	7.92189i	0.412705	−	0.299848i
$699$	−22.9357	−	6.79683i	−0.867508	−	0.257080i
$700$	−0.800859	+	0.435444i	−0.0302696	+	0.0164582i
$701$	13.1164	−	40.3682i	0.495401	−	1.52469i	−0.320930	−	0.947103i	$-0.603995\pi$
$701$	13.1164	−	40.3682i	0.495401	−	1.52469i	0.816331	−	0.577584i	$-0.196005\pi$
$702$	−18.3160	−	4.40418i	−0.691292	−	0.166225i
$703$	−53.8744			−2.03191
$704$	−1.47648	−	23.0138i	−0.0556470	−	0.867365i
$705$	−0.0599154	+	1.53185i	−0.00225654	+	0.0576930i
$706$	−7.96659	+	10.9651i	−0.299827	+	0.412676i
$707$	3.74267	−	11.5188i	0.140758	−	0.433207i
$708$	2.36169	−	3.43541i	0.0887577	−	0.129110i
$709$	−12.3701	+	8.98739i	−0.464568	+	0.337528i	−0.795321	−	0.606189i	$-0.792697\pi$
$709$	−12.3701	+	8.98739i	−0.464568	+	0.337528i	0.330753	+	0.943717i	$0.392697\pi$
$710$	0.143810	−	2.20410i	0.00539709	−	0.0827185i
$711$	0.350791	+	6.72407i	0.0131557	+	0.252172i
$712$	13.7065	−	42.1842i	0.513672	−	1.58092i
$713$	12.9019	+	9.37379i	0.483181	+	0.351051i
$714$	−0.533658	+	0.409389i	−0.0199717	+	0.0153210i
$715$	−18.0568	−	0.0196015i	−0.675285	−	0.000733055i
$716$		−	3.12916i		−	0.116942i
$717$	−16.0163	+	0.417498i	−0.598141	+	0.0155918i
$718$	−6.35880	−	2.06610i	−0.237308	−	0.0771061i
$719$	−20.6602	+	6.71290i	−0.770494	+	0.250349i	−0.667777	−	0.744362i	$-0.732754\pi$
$719$	−20.6602	+	6.71290i	−0.770494	+	0.250349i	−0.102718	+	0.994711i	$0.532754\pi$
$720$	27.8683	+	9.45821i	1.03859	+	0.352487i
$721$	−2.29467	−	3.15835i	−0.0854581	−	0.117623i
$722$	24.4774	−	7.95318i	0.910954	−	0.295987i
$723$	16.7866	−	5.94220i	0.624300	−	0.220993i
$724$	2.36963	+	1.72163i	0.0880665	+	0.0639840i
$725$	−2.23498	−	12.0192i	−0.0830050	−	0.446382i
$726$	−12.9522	+	25.2400i	−0.480699	+	0.936744i
$727$			50.7394i			1.88182i	0.338656	+	0.940910i	$0.390028\pi$
$727$			50.7394i			1.88182i	−0.338656	+	0.940910i	$0.609972\pi$
$728$	−3.19021	+	4.39095i	−0.118237	+	0.162740i
$729$	12.2406	+	24.0659i	0.453355	+	0.891330i
$730$	19.9037	−	49.9320i	0.736670	−	1.84806i
$731$	−0.606306	−	0.834508i	−0.0224250	−	0.0308654i
$732$	−2.67432	−	0.792515i	−0.0988457	−	0.0292922i
$733$	6.96380	+	21.4324i	0.257214	+	0.791623i	0.993385	+	0.114828i	$0.0366317\pi$
$733$	6.96380	+	21.4324i	0.257214	+	0.791623i	−0.736171	+	0.676795i	$0.763368\pi$
$734$	4.22024	−	12.9886i	0.155772	−	0.479417i
$735$	15.0902	−	19.1487i	0.556609	−	0.706312i
$736$			7.02803i			0.259057i
$737$	−4.35040	+	3.60804i	−0.160249	+	0.132904i
$738$	−37.9302	−	10.1730i	−1.39623	−	0.374474i
$739$	11.1028	−	15.2817i	0.408424	−	0.562148i	−0.554409	−	0.832244i	$-0.687056\pi$
$739$	11.1028	−	15.2817i	0.408424	−	0.562148i	0.962833	+	0.270097i	$0.0870556\pi$
$740$	−3.67161	+	2.31813i	−0.134971	+	0.0852163i
$741$	14.3908	−	20.9334i	0.528660	−	0.769009i
$742$	5.51181	+	7.58636i	0.202345	+	0.278504i
$743$	−22.5417	−	31.0260i	−0.826975	−	1.13823i	−0.988479	−	0.151361i	$-0.951634\pi$
$743$	−22.5417	−	31.0260i	−0.826975	−	1.13823i	0.161504	−	0.986872i	$-0.448366\pi$
$744$	7.22873	−	10.5152i	0.265018	−	0.385506i
$745$	3.04545	+	4.82359i	0.111577	+	0.176723i
$746$	27.7217	−	38.1557i	1.01496	−	1.39698i
$747$	−1.28543	−	0.344758i	−0.0470315	−	0.0126140i
$748$	−0.223194	+	0.0143193i	−0.00816078	+	0.000523566i
$749$			13.9360i			0.509211i
$750$	−13.4061	+	25.5284i	−0.489521	+	0.932164i
$751$	−0.891345	+	2.74328i	−0.0325256	+	0.100104i	−0.966001	−	0.258537i	$-0.916760\pi$
$751$	−0.891345	+	2.74328i	−0.0325256	+	0.100104i	0.933476	+	0.358641i	$0.116760\pi$
$752$	0.536616	+	1.65154i	0.0195684	+	0.0602253i
$753$	4.80987	+	1.42537i	0.175281	+	0.0519433i
$754$	5.21026	+	7.17131i	0.189746	+	0.261164i
$755$	6.06123	−	15.2057i	0.220591	−	0.553390i
$756$	−0.944453	+	0.0739913i	−0.0343494	+	0.00269104i
$757$	−21.3847	+	29.4335i	−0.777239	+	1.06978i	0.218343	+	0.975872i	$0.429935\pi$
$757$	−21.3847	+	29.4335i	−0.777239	+	1.06978i	−0.995581	+	0.0939049i	$0.970065\pi$
$758$		−	13.8584i		−	0.503358i
$759$	−16.9214	+	28.3454i	−0.614206	+	1.02887i
$760$	−22.8564	+	27.4984i	−0.829090	+	0.997472i
$761$	−3.03234	−	2.20312i	−0.109922	−	0.0798631i	0.531466	−	0.847079i	$-0.321641\pi$
$761$	−3.03234	−	2.20312i	−0.109922	−	0.0798631i	−0.641388	+	0.767216i	$0.721641\pi$
$762$	13.5067	−	4.78115i	0.489295	−	0.173203i
$763$	−13.9168	+	4.52186i	−0.503824	+	0.163702i
$764$	0.634499	+	0.873313i	0.0229554	+	0.0315953i
$765$	−0.669588	+	1.97292i	−0.0242090	+	0.0713310i
$766$	38.0807	−	12.3732i	1.37591	−	0.447061i
$767$	25.6698	+	8.34063i	0.926884	+	0.301163i
$768$	8.92000	−	0.232518i	0.321873	−	0.00839026i
$769$		−	42.5876i		−	1.53575i	−0.640602	−	0.767873i	$-0.721315\pi$
$769$		−	42.5876i		−	1.53575i	0.640602	−	0.767873i	$-0.278685\pi$
$770$	−8.82187	+	2.85582i	−0.317918	+	0.102916i
$771$	13.4943	−	10.3520i	0.485987	−	0.372819i
$772$	−2.33763	−	1.69839i	−0.0841331	−	0.0611262i
$773$	11.2114	−	34.5052i	0.403247	−	1.24107i	−0.519103	−	0.854712i	$-0.673734\pi$
$773$	11.2114	−	34.5052i	0.403247	−	1.24107i	0.922350	−	0.386355i	$-0.126266\pi$
$774$	−0.772928	−	14.8157i	−0.0277823	−	0.532540i
$775$	10.0706	+	9.54538i	0.361748	+	0.342880i
$776$	6.12770	−	4.45204i	0.219972	−	0.159819i
$777$	−7.36902	+	10.7193i	−0.264362	+	0.384551i
$778$	−5.25366	+	16.1691i	−0.188353	+	0.579690i
$779$	31.1268	−	42.8423i	1.11523	−	1.53499i
$780$	0.0800194	−	2.04585i	0.00286516	−	0.0732533i
$781$	0.544542	−	2.13179i	0.0194853	−	0.0762816i
$782$	−2.65758			−0.0950348
$783$	2.97029	−	12.3527i	0.106149	−	0.441451i
$784$	8.53392	−	26.2647i	0.304783	−	0.938026i
$785$	−4.78410	+	12.0018i	−0.170752	+	0.428361i
$786$	−5.16737	−	1.53131i	−0.184314	−	0.0546201i
$787$	26.7006	−	19.3991i	0.951772	−	0.691503i	0.000547062	−	1.00000i	$-0.499826\pi$
$787$	26.7006	−	19.3991i	0.951772	−	0.691503i	0.951225	+	0.308497i	$0.0998259\pi$
$788$	0.0182775	−	0.00593873i	0.000651110	−	0.000211558i
$789$	43.4878	−	15.3940i	1.54821	−	0.548042i
$790$	−7.24228	+	1.84158i	−0.257669	+	0.0655207i
$791$	0.101410			0.00360571
$792$	23.0252	+	12.9437i	0.818164	+	0.459936i
$793$		−	18.0588i		−	0.641286i
$794$	−16.0181	−	11.6378i	−0.568459	−	0.413010i
$795$	27.2534	+	10.0488i	0.966580	+	0.356396i
$796$	1.72760	+	5.31700i	0.0612331	+	0.188456i
$797$	−3.56521	+	2.59027i	−0.126286	+	0.0917522i	−0.649135	−	0.760673i	$-0.724869\pi$
$797$	−3.56521	+	2.59027i	−0.126286	+	0.0917522i	0.522849	+	0.852425i	$0.324869\pi$
$798$	3.70646	−	12.5073i	0.131207	−	0.442755i
$799$	−0.116919	+	0.0379894i	−0.00413631	+	0.00134397i
$800$	−0.794568	+	6.06305i	−0.0280922	+	0.214361i
$801$	31.5350	+	38.9614i	1.11423	+	1.37663i
$802$	−32.3918			−1.14379
$803$	28.6348	−	45.2448i	1.01050	−	1.59666i
$804$	−0.390068	−	0.508471i	−0.0137566	−	0.0179324i
$805$	−10.4573	+	2.65911i	−0.368572	+	0.0937213i
$806$	−9.56846	−	3.10898i	−0.337035	−	0.109509i
$807$	−0.0921845	+	0.134095i	−0.00324505	+	0.00472037i
$808$	−22.5066	−	30.9776i	−0.791778	−	1.08979i
$809$	9.62140	−	6.99036i	0.338270	−	0.245768i	−0.405661	−	0.914023i	$-0.632959\pi$
$809$	9.62140	−	6.99036i	0.338270	−	0.245768i	0.743932	+	0.668256i	$0.232959\pi$
$810$	−23.5358	+	18.5473i	−0.826963	+	0.651684i
$811$	−16.6928	−	5.42382i	−0.586164	−	0.190456i	0.000896229	−	1.00000i	$-0.499715\pi$
$811$	−16.6928	−	5.42382i	−0.586164	−	0.190456i	−0.587060	+	0.809543i	$0.699715\pi$
$812$	0.360638	+	0.262019i	0.0126559	+	0.00919506i
$813$	−17.3479	−	22.6138i	−0.608417	−	0.793100i
$814$	−41.0466	+	16.3102i	−1.43868	+	0.571674i
$815$	25.8747	+	21.5068i	0.906350	+	0.753350i
$816$	0.0614976	+	2.35921i	0.00215285	+	0.0825889i
$817$	19.0268	+	6.18218i	0.665663	+	0.216287i
$818$	8.69268	+	26.7533i	0.303932	+	0.935408i
$819$	−2.19668	−	5.72660i	−0.0767581	−	0.200104i
$820$	0.277891	−	4.25910i	0.00970438	−	0.148734i
$821$	3.71059	+	11.4200i	0.129500	+	0.398561i	0.994694	−	0.102876i	$-0.0328046\pi$
$821$	3.71059	+	11.4200i	0.129500	+	0.398561i	−0.865194	+	0.501438i	$0.832805\pi$
$822$	24.4988	−	8.67221i	0.854494	−	0.302478i
$823$	13.5738	−	18.6827i	0.473152	−	0.651238i	−0.504019	−	0.863693i	$-0.668146\pi$
$823$	13.5738	−	18.6827i	0.473152	−	0.651238i	0.977171	+	0.212454i	$0.0681457\pi$
$824$	−12.3422			−0.429962
$825$	−17.8026	+	22.5403i	−0.619807	+	0.784754i
$826$	13.8605			0.482267
$827$	−8.83432	+	12.1594i	−0.307199	+	0.422824i	−0.934505	−	0.355949i	$-0.884158\pi$
$827$	−8.83432	+	12.1594i	−0.307199	+	0.422824i	0.627306	+	0.778773i	$0.284158\pi$
$828$	−3.13879	−	2.03942i	−0.109081	−	0.0708746i
$829$	3.83757	+	11.8108i	0.133284	+	0.410207i	0.995319	−	0.0966421i	$-0.0308102\pi$
$829$	3.83757	+	11.8108i	0.133284	+	0.410207i	−0.862035	+	0.506849i	$0.830810\pi$
$830$	0.0961671	−	1.47390i	0.00333801	−	0.0511599i
$831$	−0.633264	+	2.13693i	−0.0219677	+	0.0741294i
$832$	5.23149	+	16.1009i	0.181369	+	0.558197i
$833$	1.85939	+	0.604154i	0.0644242	+	0.0209327i
$834$	2.15460	−	0.0561639i	0.0746076	−	0.00194480i
$835$	31.5201	+	26.1992i	1.09080	+	0.906662i
$836$	3.33884	−	2.76909i	0.115476	−	0.0957710i
$837$	5.51352	+	13.3243i	0.190575	+	0.460554i
$838$	−26.7904	−	19.4644i	−0.925460	−	0.672386i
$839$	−2.92227	−	0.949502i	−0.100888	−	0.0327804i	0.258138	−	0.966108i	$-0.416891\pi$
$839$	−2.92227	−	0.949502i	−0.100888	−	0.0327804i	−0.359026	+	0.933328i	$0.616891\pi$
$840$	2.34495	+	8.30896i	0.0809086	+	0.286686i
$841$	18.6250	−	13.5318i	0.642241	−	0.466615i
$842$	16.0204	+	22.0501i	0.552098	+	0.759898i
$843$	17.3121	+	11.9013i	0.596260	+	0.409903i
$844$	−4.86674	−	1.58130i	−0.167520	−	0.0544306i
$845$	−15.3255	+	3.89699i	−0.527212	+	0.134061i
$846$	−1.70780	−	0.458038i	−0.0587152	−	0.0157477i
$847$	−9.16100	+	1.18033i	−0.314776	+	0.0405567i
$848$	32.9028			1.12989
$849$	−33.8956	+	0.883557i	−1.16329	+	0.0303236i
$850$	−2.29268	−	0.300458i	−0.0786382	−	0.0103056i
$851$	−48.8812	+	15.8825i	−1.67563	+	0.544444i
$852$	0.239199	+	0.0708848i	0.00819481	+	0.00242847i
$853$	−7.35944	+	5.34694i	−0.251982	+	0.183076i	−0.706605	−	0.707608i	$-0.749774\pi$
$853$	−7.35944	+	5.34694i	−0.251982	+	0.183076i	0.454623	+	0.890684i	$0.349774\pi$
$854$	−2.86571	−	8.81973i	−0.0980624	−	0.301805i
$855$	−11.9849	−	38.5899i	−0.409876	−	1.31975i
$856$	35.6441	+	25.8970i	1.21829	+	0.885140i
$857$			16.7404i			0.571843i	0.958253	+	0.285921i	$0.0922996\pi$
$857$			16.7404i			0.571843i	−0.958253	+	0.285921i	$0.907700\pi$
$858$	4.62676	−	20.3058i	0.157955	−	0.693228i
$859$	40.7496			1.39036			0.695179	−	0.718836i	$-0.255325\pi$
$859$	40.7496			1.39036			0.695179	+	0.718836i	$0.255325\pi$
$860$	1.56271	−	0.397370i	0.0532879	−	0.0135502i
$861$	−4.26667	−	12.0532i	−0.145408	−	0.410774i
$862$	32.6194	−	10.5987i	1.11102	−	0.360993i
$863$	−0.766527	+	0.556915i	−0.0260929	+	0.0189576i	−0.600755	−	0.799433i	$-0.705133\pi$
$863$	−0.766527	+	0.556915i	−0.0260929	+	0.0189576i	0.574662	+	0.818391i	$0.305133\pi$
$864$	−3.32230	+	5.41716i	−0.113027	+	0.184295i
$865$	−4.04033	+	10.1359i	−0.137375	+	0.344630i
$866$	11.0577	−	34.0321i	0.375756	−	1.15646i
$867$	29.2678	−	0.762925i	0.993988	−	0.0259103i
$868$	−0.505951			−0.0171731
$869$	−7.42857	+	0.476591i	−0.251997	+	0.0161672i
$870$	14.0895	+	0.551082i	0.477678	+	0.0186834i
$871$	2.43880	−	3.35672i	0.0826355	−	0.113738i
$872$	−14.2958	+	43.9979i	−0.484116	+	1.48996i
$873$	0.445934	+	8.54780i	0.0150926	+	0.289299i
$874$	41.6994	−	30.2964i	1.41050	−	1.02479i
$875$	−9.32210	+	1.11173i	−0.315145	+	0.0375833i
$876$	5.00313	+	3.43943i	0.169040	+	0.116208i
$877$	−3.81384	+	11.7378i	−0.128784	+	0.396357i	−0.994572	−	0.104055i	$-0.966818\pi$
$877$	−3.81384	+	11.7378i	−0.128784	+	0.396357i	0.865787	+	0.500412i	$0.166818\pi$
$878$	−27.5419	−	20.0104i	−0.929495	−	0.675318i
$879$	9.79563	+	12.7691i	0.330398	+	0.430689i
$880$	−10.0876	+	30.9323i	−0.340054	+	1.04273i
$881$			28.7037i			0.967052i	0.875330	+	0.483526i	$0.160644\pi$
$881$			28.7037i			0.967052i	−0.875330	+	0.483526i	$0.839356\pi$
$882$	17.6909	+	21.8570i	0.595682	+	0.735964i
$883$	29.0294	+	9.43222i	0.976916	+	0.317419i	0.753605	−	0.657328i	$-0.228313\pi$
$883$	29.0294	+	9.43222i	0.976916	+	0.317419i	0.223312	+	0.974747i	$0.428313\pi$
$884$	0.156151	−	0.0507364i	0.00525191	−	0.00170645i
$885$	35.6942	−	23.8593i	1.19985	−	0.802020i
$886$	7.39579	+	10.1794i	0.248466	+	0.341985i
$887$	−30.7573	+	9.99365i	−1.03273	+	0.335554i	−0.775869	−	0.630894i	$-0.782688\pi$
$887$	−30.7573	+	9.99365i	−1.03273	+	0.335554i	−0.256860	+	0.966449i	$0.582688\pi$
$888$	13.7229	+	38.7670i	0.460512	+	1.30094i
$889$	3.77408	+	2.74203i	0.126578	+	0.0919646i
$890$	−35.5591	+	42.7809i	−1.19194	+	1.43402i
$891$	−26.4423	+	13.8494i	−0.885851	+	0.463971i
$892$			4.38574i			0.146845i
$893$	1.40147	−	1.92896i	0.0468985	−	0.0645503i
$894$	−6.20235	+	2.19554i	−0.207438	+	0.0734297i
$895$	11.9329	−	29.9357i	0.398872	−	1.00064i
$896$	6.31726	+	8.69496i	0.211045	+	0.290478i
$897$	6.88574	−	23.2357i	0.229908	−	0.775819i
$898$	9.68016	+	29.7925i	0.323031	+	0.994187i
$899$	2.09677	−	6.45320i	0.0699312	−	0.215226i
$900$	−2.47725	−	2.11426i	−0.0825750	−	0.0704752i
$901$			2.32934i			0.0776014i
$902$	10.7450	−	42.0648i	0.357768	−	1.40060i
$903$	3.83256	−	2.94010i	0.127540	−	0.0978405i
$904$	0.188447	−	0.259375i	0.00626765	−	0.00862668i
$905$	16.1041	+	25.5067i	0.535319	+	0.847873i
$906$	15.5581	+	10.6955i	0.516882	+	0.355334i
$907$	1.94785	+	2.68099i	0.0646774	+	0.0890208i	0.840130	−	0.542385i	$-0.182478\pi$
$907$	1.94785	+	2.68099i	0.0646774	+	0.0890208i	−0.775453	+	0.631405i	$0.782478\pi$
$908$	−0.0823649	−	0.113365i	−0.00273337	−	0.00376217i
$909$	43.2120	−	2.25435i	1.43325	−	0.0747721i
$910$	5.75591	−	3.63409i	0.190806	−	0.120469i
$911$	−20.3107	+	27.9553i	−0.672923	+	0.926200i	−0.999822	−	0.0188597i	$-0.993996\pi$
$911$	−20.3107	+	27.9553i	−0.672923	+	0.926200i	0.326899	+	0.945059i	$0.393996\pi$
$912$	−27.8599	−	36.3167i	−0.922535	−	1.20257i
$913$	0.364141	−	1.42555i	0.0120513	−	0.0471788i
$914$			43.1968i			1.42882i
$915$	−22.5621	−	17.7801i	−0.745881	−	0.587792i
$916$	1.24364	−	3.82754i	0.0410911	−	0.126465i
$917$	−0.542251	−	1.66888i	−0.0179067	−	0.0551112i
$918$	−2.04844	−	1.25629i	−0.0676086	−	0.0414638i
$919$	24.5699	+	33.8175i	0.810485	+	1.11554i	0.991248	+	0.132010i	$0.0421432\pi$
$919$	24.5699	+	33.8175i	0.810485	+	1.11554i	−0.180763	+	0.983527i	$0.557857\pi$
$920$	−12.6314	+	31.6880i	−0.416444	+	1.04472i
$921$	−13.3497	−	37.7127i	−0.439889	−	1.24268i
$922$	14.8220	−	20.4007i	0.488137	−	0.671863i
$923$			1.61523i			0.0531659i
$924$	−0.0942679	−	1.04308i	−0.00310119	−	0.0343148i
$925$	−43.9652	+	8.17536i	−1.44557	+	0.268804i
$926$	13.8433	+	10.0577i	0.454919	+	0.330518i
$927$	7.59916	−	11.6956i	0.249589	−	0.384134i
$928$	2.84388	−	0.924034i	0.0933551	−	0.0303329i
$929$	−20.2691	−	27.8981i	−0.665009	−	0.915306i	0.334626	−	0.942351i	$-0.391390\pi$
$929$	−20.2691	−	27.8981i	−0.665009	−	0.915306i	−0.999634	+	0.0270453i	$0.991390\pi$
$930$	−13.3051	+	8.89357i	−0.436290	+	0.291632i
$931$	−36.0626	+	11.7175i	−1.18191	+	0.384024i
$932$	2.85192	+	0.926646i	0.0934179	+	0.0303533i
$933$	−0.695844	−	26.6944i	−0.0227809	−	0.873936i
$934$		−	47.0002i		−	1.53789i
$935$	−2.18983	−	0.714148i	−0.0716151	−	0.0233551i
$936$	−18.7289	−	5.02318i	−0.612175	−	0.164188i
$937$	−21.7268	−	15.7854i	−0.709782	−	0.515687i	0.173321	−	0.984865i	$-0.444550\pi$
$937$	−21.7268	−	15.7854i	−0.709782	−	0.515687i	−0.883103	+	0.469178i	$0.844550\pi$
$938$	0.658416	−	2.02640i	0.0214980	−	0.0661642i
$939$	18.9866	−	27.6186i	0.619604	−	0.901300i
$940$	0.0125120	−	0.191764i	0.000408095	−	0.00625467i
$941$	−12.3620	+	8.98151i	−0.402989	+	0.292789i	−0.770757	−	0.637129i	$-0.780122\pi$
$941$	−12.3620	+	8.98151i	−0.402989	+	0.292789i	0.367768	+	0.929917i	$0.380122\pi$
$942$	−12.2799	−	8.44190i	−0.400101	−	0.275052i
$943$	15.6117	−	48.0479i	0.508387	−	1.56466i
$944$	28.5860	−	39.3453i	0.930396	−	1.28058i
$945$	−9.31744	−	2.89376i	−0.303096	−	0.0941341i
$946$	16.3680	−	1.05011i	0.532170	−	0.0341421i
$947$	0.270360			0.00878553			0.00439276	−	0.999990i	$-0.498602\pi$
$947$	0.270360			0.00878553			0.00439276	+	0.999990i	$0.498602\pi$
$948$	−0.0219941	−	0.843754i	−0.000714337	−	0.0274039i
$949$	−12.1468	+	37.3841i	−0.394303	+	1.21354i
$950$	39.3991	−	21.4221i	1.27827	−	0.695026i
$951$	5.71115	−	19.2721i	0.185197	−	0.624941i
$952$	−0.560113	+	0.406946i	−0.0181534	+	0.0131892i
$953$	−34.7003	+	11.2748i	−1.12405	+	0.365227i	−0.811314	−	0.584611i	$-0.801247\pi$
$953$	−34.7003	+	11.2748i	−1.12405	+	0.365227i	−0.312741	+	0.949839i	$0.601247\pi$
$954$	−18.2532	+	28.0929i	−0.590970	+	0.909540i
$955$	2.73972	+	10.7743i	0.0886553	+	0.348649i
$956$	2.00841			0.0649566
$957$	13.6947	+	3.12040i	0.442687	+	0.100868i
$958$			12.8401i			0.414844i
$959$	6.84554	+	4.97358i	0.221054	+	0.160605i
$960$	25.2667	+	9.31632i	0.815481	+	0.300683i
$961$	−7.19970	−	22.1584i	−0.232248	−	0.714787i
$962$	26.2320	−	19.0587i	0.845755	−	0.614477i
$963$	−46.4864	+	17.8318i	−1.49800	+	0.574621i
$964$	−2.12298	+	0.689797i	−0.0683765	+	0.0222169i
$965$	−15.8866	−	25.1623i	−0.511409	−	0.810004i
$966$	−0.324294	−	12.4408i	−0.0104340	−	0.400276i
$967$	−26.8506			−0.863457			−0.431729	−	0.902004i	$-0.642096\pi$
$967$	−26.8506			−0.863457			−0.431729	+	0.902004i	$0.642096\pi$
$968$	−14.0047	+	25.6244i	−0.450129	+	0.823600i
$969$	2.57102	−	1.97233i	0.0825930	−	0.0633603i
$970$	−9.20657	+	2.34107i	−0.295605	+	0.0751672i
$971$	23.6646	+	7.68908i	0.759432	+	0.246754i	0.663035	−	0.748589i	$-0.269268\pi$
$971$	23.6646	+	7.68908i	0.759432	+	0.246754i	0.0963971	+	0.995343i	$0.469268\pi$
$972$	−1.45528	−	3.05574i	−0.0466783	−	0.0980128i
$973$	0.412479	+	0.567729i	0.0132235	+	0.0182006i
$974$	43.9827	−	31.9553i	1.40930	−	1.02391i
$975$	8.56726	−	19.2669i	0.274372	−	0.617034i
$976$	−30.9466	−	10.0552i	−0.990577	−	0.321858i
$977$	−42.1021	−	30.5889i	−1.34696	−	0.978627i	−0.999157	−	0.0410613i	$-0.986926\pi$
$977$	−42.1021	−	30.5889i	−1.34696	−	0.978627i	−0.347808	−	0.937566i	$-0.613074\pi$
$978$	−30.7898	+	23.6201i	−0.984551	+	0.755286i
$979$	−42.6539	+	35.3753i	−1.36322	+	1.13060i
$980$	−1.95353	+	2.35028i	−0.0624032	+	0.0750769i
$981$	−32.8908	−	40.6365i	−1.05012	−	1.29742i
$982$	−53.0630	−	17.2412i	−1.69331	−	0.550190i
$983$	11.4114	+	35.1206i	0.363966	+	1.12017i	0.950626	+	0.310339i	$0.100443\pi$
$983$	11.4114	+	35.1206i	0.363966	+	1.12017i	−0.586660	+	0.809833i	$0.699557\pi$
$984$	−38.7572	−	11.4854i	−1.23553	−	0.366141i
$985$	0.197502	+	0.0128863i	0.00629294	+	0.000410592i
$986$	0.349414	+	1.07538i	0.0111276	+	0.0342472i
$987$	−0.192105	−	0.542694i	−0.00611478	−	0.0172741i
$988$	−1.87172	+	2.57621i	−0.0595475	+	0.0819601i
$989$	19.0859			0.606895
$990$	−20.8141	−	25.7730i	−0.661517	−	0.819119i
$991$	−45.1756			−1.43505			−0.717525	−	0.696533i	$-0.754725\pi$
$991$	−45.1756			−1.43505			−0.717525	+	0.696533i	$0.754725\pi$
$992$	−1.99489	+	2.74573i	−0.0633379	+	0.0871771i
$993$	2.36355	+	6.67697i	0.0750049	+	0.211887i
$994$	0.256317	+	0.788862i	0.00812987	+	0.0250212i
$995$	−3.74868	+	57.4541i	−0.118841	+	1.82142i
$996$	0.159954	+	0.0474013i	0.00506835	+	0.00150197i
$997$	10.5742	+	32.5440i	0.334888	+	1.03068i	0.966777	+	0.255621i	$0.0822798\pi$
$997$	10.5742	+	32.5440i	0.334888	+	1.03068i	−0.631889	+	0.775059i	$0.717720\pi$
$998$	3.06691	+	0.996500i	0.0970814	+	0.0315437i
$999$	−45.1853	−	10.8651i	−1.42960	−	0.343755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.r.a.29.16	yes	80
3.2	odd	2	inner	165.2.r.a.29.6	yes	80
5.2	odd	4		825.2.bi.h.326.16		80
5.3	odd	4		825.2.bi.h.326.5		80
5.4	even	2	inner	165.2.r.a.29.5	✓	80
11.8	odd	10	inner	165.2.r.a.74.15	yes	80
15.2	even	4		825.2.bi.h.326.6		80
15.8	even	4		825.2.bi.h.326.15		80
15.14	odd	2	inner	165.2.r.a.29.15	yes	80
33.8	even	10	inner	165.2.r.a.74.5	yes	80
55.8	even	20		825.2.bi.h.701.15		80
55.19	odd	10	inner	165.2.r.a.74.6	yes	80
55.52	even	20		825.2.bi.h.701.6		80
165.8	odd	20		825.2.bi.h.701.5		80
165.74	even	10	inner	165.2.r.a.74.16	yes	80
165.107	odd	20		825.2.bi.h.701.16		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.29.5	✓	80	5.4	even	2	inner
165.2.r.a.29.6	yes	80	3.2	odd	2	inner
165.2.r.a.29.15	yes	80	15.14	odd	2	inner
165.2.r.a.29.16	yes	80	1.1	even	1	trivial
165.2.r.a.74.5	yes	80	33.8	even	10	inner
165.2.r.a.74.6	yes	80	55.19	odd	10	inner
165.2.r.a.74.15	yes	80	11.8	odd	10	inner
165.2.r.a.74.16	yes	80	165.74	even	10	inner
825.2.bi.h.326.5		80	5.3	odd	4
825.2.bi.h.326.6		80	15.2	even	4
825.2.bi.h.326.15		80	15.8	even	4
825.2.bi.h.326.16		80	5.2	odd	4
825.2.bi.h.701.5		80	165.8	odd	20
825.2.bi.h.701.6		80	55.52	even	20
825.2.bi.h.701.15		80	55.8	even	20
825.2.bi.h.701.16		80	165.107	odd	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.875212 - 1.20463i) q^{2} +(0.577976 + 1.63277i) q^{3} +(-0.0670941 - 0.206494i) q^{4} +(0.145586 - 2.23132i) q^{5} +(2.47273 + 0.732776i) q^{6} +(0.259482 + 0.798604i) q^{7} +(2.52478 + 0.820350i) q^{8} +(-2.33189 + 1.88741i) q^{9} +O(q^{10})\)	\(q+(0.875212 - 1.20463i) q^{2} +(0.577976 + 1.63277i) q^{3} +(-0.0670941 - 0.206494i) q^{4} +(0.145586 - 2.23132i) q^{5} +(2.47273 + 0.732776i) q^{6} +(0.259482 + 0.798604i) q^{7} +(2.52478 + 0.820350i) q^{8} +(-2.33189 + 1.88741i) q^{9} +(-2.56049 - 2.12826i) q^{10} +(-2.11726 - 2.55289i) q^{11} +(0.298379 - 0.228898i) q^{12} +(1.96978 + 1.43113i) q^{13} +(1.18912 + 0.386369i) q^{14} +(3.72739 - 1.05194i) q^{15} +(3.54924 - 2.57867i) q^{16} +(0.182555 + 0.251266i) q^{17} +(0.232725 + 4.46093i) q^{18} +(-5.72886 - 1.86142i) q^{19} +(-0.470524 + 0.119646i) q^{20} +(-1.15396 + 0.885250i) q^{21} +(-4.92832 + 0.316183i) q^{22} -5.74665 q^{23} +(0.119818 + 4.59653i) q^{24} +(-4.95761 - 0.649699i) q^{25} +(3.44794 - 1.12031i) q^{26} +(-4.42948 - 2.71656i) q^{27} +(0.147498 - 0.107163i) q^{28} +(0.755560 + 2.32538i) q^{29} +(1.99506 - 5.41078i) q^{30} +(-2.24512 - 1.63117i) q^{31} -1.22298i q^{32} +(2.94456 - 4.93250i) q^{33} +0.462456 q^{34} +(1.81972 - 0.462723i) q^{35} +(0.546194 + 0.354887i) q^{36} +(8.50603 - 2.76378i) q^{37} +(-7.25629 + 5.27200i) q^{38} +(-1.19822 + 4.04335i) q^{39} +(2.19804 - 5.51416i) q^{40} +(-2.71666 + 8.36103i) q^{41} +(0.0564319 + 2.16488i) q^{42} -3.32121 q^{43} +(-0.385101 + 0.608485i) q^{44} +(3.87193 + 5.47797i) q^{45} +(-5.02954 + 6.92257i) q^{46} +(-0.122317 + 0.376453i) q^{47} +(6.26176 + 4.30468i) q^{48} +(5.09268 - 3.70005i) q^{49} +(-5.12161 + 5.40344i) q^{50} +(-0.304747 + 0.443297i) q^{51} +(0.163359 - 0.502768i) q^{52} +(6.06755 + 4.40833i) q^{53} +(-7.14918 + 2.95830i) q^{54} +(-6.00456 + 4.35262i) q^{55} +2.22916i q^{56} +(-0.271873 - 10.4298i) q^{57} +(3.46248 + 1.12503i) q^{58} +(10.5430 - 3.42562i) q^{59} +(-0.467306 - 0.699105i) q^{60} +(-4.35961 - 6.00049i) q^{61} +(-3.92991 + 1.27691i) q^{62} +(-2.11237 - 1.37251i) q^{63} +(5.62525 + 4.08698i) q^{64} +(3.48008 - 4.18686i) q^{65} +(-3.36471 - 7.86408i) q^{66} -1.70411i q^{67} +(0.0396366 - 0.0545551i) q^{68} +(-3.32143 - 9.38297i) q^{69} +(1.03523 - 2.59707i) q^{70} +(0.389936 + 0.536701i) q^{71} +(-7.43583 + 2.85232i) q^{72} +(4.98888 + 15.3542i) q^{73} +(4.11526 - 12.6655i) q^{74} +(-1.80457 - 8.47015i) q^{75} +1.30787i q^{76} +(1.48936 - 2.35328i) q^{77} +(3.82203 + 4.98220i) q^{78} +(1.31923 - 1.81576i) q^{79} +(-5.23713 - 8.29492i) q^{80} +(1.87539 - 8.80244i) q^{81} +(7.69425 + 10.5902i) q^{82} +(0.260754 + 0.358897i) q^{83} +(0.260223 + 0.178892i) q^{84} +(0.587233 - 0.370759i) q^{85} +(-2.90677 + 4.00082i) q^{86} +(-3.36011 + 2.57767i) q^{87} +(-3.25134 - 8.18236i) q^{88} -16.7081i q^{89} +(9.98767 + 0.130166i) q^{90} +(-0.631782 + 1.94442i) q^{91} +(0.385566 + 1.18665i) q^{92} +(1.36571 - 4.60855i) q^{93} +(0.346431 + 0.476822i) q^{94} +(-4.98748 + 12.5120i) q^{95} +(1.99684 - 0.706853i) q^{96} +(1.67704 - 2.30824i) q^{97} -9.37311i q^{98} +(9.75554 + 1.95692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9}+O(q^{10}) \) 80 * q + 4 * q^4 - 10 * q^6 - 10 * q^9	\( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} - 2 q^{15} - 60 q^{16} - 20 q^{19} - 30 q^{24} + 6 q^{25} + 10 q^{30} - 20 q^{31} - 56 q^{34} + 2 q^{36} - 50 q^{39} + 60 q^{40} - 92 q^{45} - 40 q^{46} + 72 q^{49} + 30 q^{51} + 4 q^{55} + 54 q^{60} + 96 q^{64} - 42 q^{66} + 30 q^{69} - 86 q^{70} + 2 q^{75} - 66 q^{81} + 140 q^{84} - 30 q^{85} + 120 q^{90} + 48 q^{91} + 60 q^{94} - 70 q^{96} + 60 q^{99}+O(q^{100}) \) 80 * q + 4 * q^4 - 10 * q^6 - 10 * q^9 - 2 * q^15 - 60 * q^16 - 20 * q^19 - 30 * q^24 + 6 * q^25 + 10 * q^30 - 20 * q^31 - 56 * q^34 + 2 * q^36 - 50 * q^39 + 60 * q^40 - 92 * q^45 - 40 * q^46 + 72 * q^49 + 30 * q^51 + 4 * q^55 + 54 * q^60 + 96 * q^64 - 42 * q^66 + 30 * q^69 - 86 * q^70 + 2 * q^75 - 66 * q^81 + 140 * q^84 - 30 * q^85 + 120 * q^90 + 48 * q^91 + 60 * q^94 - 70 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

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