LMFDB - Embedded newform 960.2.cn.a.131.123

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.123
Character	$\chi$	$=$	960.131
Dual form			960.2.cn.a.491.123

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39335 - 0.242001i) q^{2} +(-1.69740 + 0.344744i) q^{3} +(1.88287 - 0.674385i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(-2.28164 + 0.891121i) q^{6} +(-0.799862 - 1.93104i) q^{7} +(2.46030 - 1.39531i) q^{8} +(2.76230 - 1.17033i) q^{9} +O(q^{10})$	\(q+(1.39335 - 0.242001i) q^{2} +(-1.69740 + 0.344744i) q^{3} +(1.88287 - 0.674385i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(-2.28164 + 0.891121i) q^{6} +(-0.799862 - 1.93104i) q^{7} +(2.46030 - 1.39531i) q^{8} +(2.76230 - 1.17033i) q^{9} +(-0.572890 + 1.29298i) q^{10} +(-0.887886 + 0.176611i) q^{11} +(-2.96349 + 1.79381i) q^{12} +(-1.65449 + 1.10549i) q^{13} +(-1.58180 - 2.49705i) q^{14} +(0.656379 - 1.60286i) q^{15} +(3.09041 - 2.53956i) q^{16} +(5.29459 - 5.29459i) q^{17} +(3.56565 - 2.29917i) q^{18} +(0.695437 - 0.464676i) q^{19} +(-0.485336 + 1.94022i) q^{20} +(2.02340 + 3.00199i) q^{21} +(-1.19440 + 0.460951i) q^{22} +(0.779821 - 1.88265i) q^{23} +(-3.69508 + 3.21657i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(-2.03776 + 1.94073i) q^{26} +(-4.28526 + 2.93880i) q^{27} +(-2.80830 - 3.09648i) q^{28} +(1.12634 - 5.66248i) q^{29} +(0.526674 - 2.39220i) q^{30} -0.323024 q^{31} +(3.69146 - 4.28639i) q^{32} +(1.44621 - 0.605873i) q^{33} +(6.09595 - 8.65854i) q^{34} +(2.04998 + 0.407766i) q^{35} +(4.41181 - 4.06644i) q^{36} +(1.85269 - 2.77275i) q^{37} +(0.856538 - 0.815754i) q^{38} +(2.42721 - 2.44684i) q^{39} +(-0.206711 + 2.82086i) q^{40} +(8.87914 + 3.67786i) q^{41} +(3.54579 + 3.69317i) q^{42} +(2.67492 - 0.532075i) q^{43} +(-1.55267 + 0.931314i) q^{44} +(-0.561557 + 2.94697i) q^{45} +(0.630963 - 2.81192i) q^{46} +(-5.05588 - 5.05588i) q^{47} +(-4.37015 + 5.37604i) q^{48} +(1.86062 - 1.86062i) q^{49} +(-0.756793 - 1.19468i) q^{50} +(-7.16174 + 10.8123i) q^{51} +(-2.36966 + 3.19727i) q^{52} +(-0.647422 - 3.25481i) q^{53} +(-5.25969 + 5.13183i) q^{54} +(0.346436 - 0.836370i) q^{55} +(-4.66231 - 3.63488i) q^{56} +(-1.02024 + 1.02849i) q^{57} +(0.199063 - 8.16242i) q^{58} +(-1.86859 - 1.24855i) q^{59} +(0.154930 - 3.46064i) q^{60} +(-2.77520 + 13.9519i) q^{61} +(-0.450087 + 0.0781721i) q^{62} +(-4.46942 - 4.39801i) q^{63} +(4.10620 - 6.86579i) q^{64} -1.98984i q^{65} +(1.86846 - 1.19418i) q^{66} +(0.225754 + 0.0449052i) q^{67} +(6.39844 - 13.5396i) q^{68} +(-0.674631 + 3.46445i) q^{69} +(2.95503 + 0.0720664i) q^{70} +(1.58369 - 0.655987i) q^{71} +(5.16313 - 6.73366i) q^{72} +(1.69340 + 0.701430i) q^{73} +(1.91045 - 4.31177i) q^{74} +(0.968067 + 1.43626i) q^{75} +(0.996047 - 1.34392i) q^{76} +(1.05123 + 1.57328i) q^{77} +(2.78983 - 3.99670i) q^{78} +(2.86075 + 2.86075i) q^{79} +(0.394629 + 3.98049i) q^{80} +(6.26064 - 6.46563i) q^{81} +(13.2618 + 2.97580i) q^{82} +(-5.69890 - 8.52901i) q^{83} +(5.83429 + 4.28781i) q^{84} +(1.46078 + 7.34381i) q^{85} +(3.59835 - 1.38870i) q^{86} +(0.0402645 + 9.99977i) q^{87} +(-1.93804 + 1.67340i) q^{88} +(0.568334 - 0.235412i) q^{89} +(-0.0692786 + 4.24208i) q^{90} +(3.45812 + 2.31064i) q^{91} +(0.198668 - 4.07070i) q^{92} +(0.548300 - 0.111361i) q^{93} +(-8.26816 - 5.82111i) q^{94} +0.836395i q^{95} +(-4.78816 + 8.54831i) q^{96} +7.81094i q^{97} +(2.14223 - 3.04277i) q^{98} +(-2.24592 + 1.52698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.39335	−	0.242001i	0.985250	−	0.171120i
$2$	1.39335	−	0.242001i	0.985250	−	0.171120i
$3$	−1.69740	+	0.344744i	−0.979992	+	0.199038i
$3$	−1.69740	+	0.344744i	−0.979992	+	0.199038i
$4$	1.88287	−	0.674385i	0.941436	−	0.337193i
$5$	−0.555570	+	0.831470i	−0.248459	+	0.371845i
$5$	−0.555570	+	0.831470i	−0.248459	+	0.371845i
$6$	−2.28164	+	0.891121i	−0.931478	+	0.363799i
$7$	−0.799862	−	1.93104i	−0.302319	−	0.729864i	−0.999911	−	0.0133678i	$-0.995745\pi$
$7$	−0.799862	−	1.93104i	−0.302319	−	0.729864i	0.697591	−	0.716496i	$-0.254255\pi$
$8$	2.46030	−	1.39531i	0.869849	−	0.493318i
$9$	2.76230	−	1.17033i	0.920768	−	0.390111i
$10$	−0.572890	+	1.29298i	−0.181164	+	0.408876i
$11$	−0.887886	+	0.176611i	−0.267708	+	0.0532504i	−0.327119	−	0.944983i	$-0.606078\pi$
$11$	−0.887886	+	0.176611i	−0.267708	+	0.0532504i	0.0594111	+	0.998234i	$0.481078\pi$
$12$	−2.96349	+	1.79381i	−0.855485	+	0.517827i
$13$	−1.65449	+	1.10549i	−0.458873	+	0.306609i	−0.763436	−	0.645883i	$-0.776489\pi$
$13$	−1.65449	+	1.10549i	−0.458873	+	0.306609i	0.304563	+	0.952492i	$0.401489\pi$
$14$	−1.58180	−	2.49705i	−0.422755	−	0.667365i
$15$	0.656379	−	1.60286i	0.169476	−	0.413857i
$16$	3.09041	−	2.53956i	0.772602	−	0.634890i
$17$	5.29459	−	5.29459i	1.28413	−	1.28413i	0.345831	−	0.938297i	$-0.387597\pi$
$17$	5.29459	−	5.29459i	1.28413	−	1.28413i	0.938297	−	0.345831i	$-0.112403\pi$
$18$	3.56565	−	2.29917i	0.840431	−	0.541919i
$19$	0.695437	−	0.464676i	0.159544	−	0.106604i	−0.473235	−	0.880936i	$-0.656914\pi$
$19$	0.695437	−	0.464676i	0.159544	−	0.106604i	0.632779	+	0.774332i	$0.281914\pi$
$20$	−0.485336	+	1.94022i	−0.108525	+	0.433846i
$21$	2.02340	+	3.00199i	0.441541	+	0.655088i
$22$	−1.19440	+	0.460951i	−0.254647	+	0.0982751i
$23$	0.779821	−	1.88265i	0.162604	−	0.392561i	−0.821487	−	0.570228i	$-0.806855\pi$
$23$	0.779821	−	1.88265i	0.162604	−	0.392561i	0.984091	+	0.177667i	$0.0568550\pi$
$24$	−3.69508	+	3.21657i	−0.754256	+	0.656580i
$25$	−0.382683	−	0.923880i	−0.0765367	−	0.184776i
$26$	−2.03776	+	1.94073i	−0.399638	+	0.380609i
$27$	−4.28526	+	2.93880i	−0.824698	+	0.565573i
$28$	−2.80830	−	3.09648i	−0.530719	−	0.585180i
$29$	1.12634	−	5.66248i	0.209156	−	1.05150i	−0.723389	−	0.690441i	$-0.757417\pi$
$29$	1.12634	−	5.66248i	0.209156	−	1.05150i	0.932544	−	0.361055i	$-0.117583\pi$
$30$	0.526674	−	2.39220i	0.0961571	−	0.436754i
$31$	−0.323024			−0.0580169			−0.0290084	−	0.999579i	$-0.509235\pi$
$31$	−0.323024			−0.0580169			−0.0290084	+	0.999579i	$0.509235\pi$
$32$	3.69146	−	4.28639i	0.652564	−	0.757734i
$33$	1.44621	−	0.605873i	0.251752	−	0.105469i
$34$	6.09595	−	8.65854i	1.04545	−	1.48493i
$35$	2.04998	+	0.407766i	0.346510	+	0.0689251i
$36$	4.41181	−	4.06644i	0.735301	−	0.677741i
$37$	1.85269	−	2.77275i	0.304581	−	0.455837i	−0.647331	−	0.762209i	$-0.724115\pi$
$37$	1.85269	−	2.77275i	0.304581	−	0.455837i	0.951912	+	0.306372i	$0.0991150\pi$
$38$	0.856538	−	0.815754i	0.138949	−	0.132333i
$39$	2.42721	−	2.44684i	0.388665	−	0.391808i
$40$	−0.206711	+	2.82086i	−0.0326839	+	0.446018i
$41$	8.87914	+	3.67786i	1.38669	+	0.574385i	0.946261	−	0.323403i	$-0.104827\pi$
$41$	8.87914	+	3.67786i	1.38669	+	0.574385i	0.440427	+	0.897788i	$0.354827\pi$
$42$	3.54579	+	3.69317i	0.547127	+	0.569868i
$43$	2.67492	−	0.532075i	0.407922	−	0.0811407i	0.0131356	−	0.999914i	$-0.495819\pi$
$43$	2.67492	−	0.532075i	0.407922	−	0.0811407i	0.394786	+	0.918773i	$0.370819\pi$
$44$	−1.55267	+	0.931314i	−0.234074	+	0.140401i
$45$	−0.561557	+	2.94697i	−0.0837120	+	0.439309i
$46$	0.630963	−	2.81192i	0.0930304	−	0.414595i
$47$	−5.05588	−	5.05588i	−0.737476	−	0.737476i	0.234613	−	0.972089i	$-0.424618\pi$
$47$	−5.05588	−	5.05588i	−0.737476	−	0.737476i	−0.972089	+	0.234613i	$0.924618\pi$
$48$	−4.37015	+	5.37604i	−0.630777	+	0.775964i
$49$	1.86062	−	1.86062i	0.265803	−	0.265803i
$50$	−0.756793	−	1.19468i	−0.107027	−	0.168954i
$51$	−7.16174	+	10.8123i	−1.00284	+	1.51402i
$52$	−2.36966	+	3.19727i	−0.328613	+	0.443381i
$53$	−0.647422	−	3.25481i	−0.0889302	−	0.447082i	−0.999436	−	0.0335857i	$-0.989307\pi$
$53$	−0.647422	−	3.25481i	−0.0889302	−	0.447082i	0.910506	−	0.413497i	$-0.135693\pi$
$54$	−5.25969	+	5.13183i	−0.715753	+	0.698354i
$55$	0.346436	−	0.836370i	0.0467134	−	0.112776i
$56$	−4.66231	−	3.63488i	−0.623027	−	0.485732i
$57$	−1.02024	+	1.02849i	−0.135134	+	0.136226i
$58$	0.199063	−	8.16242i	0.0261382	−	1.07178i
$59$	−1.86859	−	1.24855i	−0.243269	−	0.162547i	0.427959	−	0.903798i	$-0.359233\pi$
$59$	−1.86859	−	1.24855i	−0.243269	−	0.162547i	−0.671228	+	0.741251i	$0.734233\pi$
$60$	0.154930	−	3.46064i	0.0200013	−	0.446766i
$61$	−2.77520	+	13.9519i	−0.355328	+	1.78635i	0.227520	+	0.973773i	$0.426938\pi$
$61$	−2.77520	+	13.9519i	−0.355328	+	1.78635i	−0.582848	+	0.812581i	$0.698062\pi$
$62$	−0.450087	+	0.0781721i	−0.0571611	+	0.00992786i
$63$	−4.46942	−	4.39801i	−0.563094	−	0.554097i
$64$	4.10620	−	6.86579i	0.513275	−	0.858224i
$65$		−	1.98984i		−	0.246809i
$66$	1.86846	−	1.19418i	0.229991	−	0.146993i
$67$	0.225754	+	0.0449052i	0.0275802	+	0.00548604i	0.208861	−	0.977945i	$-0.433024\pi$
$67$	0.225754	+	0.0449052i	0.0275802	+	0.00548604i	−0.181281	+	0.983431i	$0.558024\pi$
$68$	6.39844	−	13.5396i	0.775925	−	1.64192i
$69$	−0.674631	+	3.46445i	−0.0812161	+	0.417070i
$70$	2.95503	+	0.0720664i	0.353193	+	0.00861358i
$71$	1.58369	−	0.655987i	0.187950	−	0.0778513i	−0.286724	−	0.958013i	$-0.592566\pi$
$71$	1.58369	−	0.655987i	0.187950	−	0.0778513i	0.474673	+	0.880162i	$0.342566\pi$
$72$	5.16313	−	6.73366i	0.608480	−	0.793569i
$73$	1.69340	+	0.701430i	0.198198	+	0.0820962i	0.479574	−	0.877501i	$-0.340791\pi$
$73$	1.69340	+	0.701430i	0.198198	+	0.0820962i	−0.281377	+	0.959597i	$0.590791\pi$
$74$	1.91045	−	4.31177i	0.222085	−	0.501233i
$75$	0.968067	+	1.43626i	0.111783	+	0.165845i
$76$	0.996047	−	1.34392i	0.114254	−	0.154158i
$77$	1.05123	+	1.57328i	0.119799	+	0.179292i
$78$	2.78983	−	3.99670i	0.315886	−	0.452537i
$79$	2.86075	+	2.86075i	0.321859	+	0.321859i	0.849480	−	0.527621i	$-0.176916\pi$
$79$	2.86075	+	2.86075i	0.321859	+	0.321859i	−0.527621	+	0.849480i	$0.676916\pi$
$80$	0.394629	+	3.98049i	0.0441209	+	0.445032i
$81$	6.26064	−	6.46563i	0.695627	−	0.718403i
$82$	13.2618	+	2.97580i	1.46452	+	0.328622i
$83$	−5.69890	−	8.52901i	−0.625536	−	0.936180i	−0.999960	−	0.00892294i	$-0.997160\pi$
$83$	−5.69890	−	8.52901i	−0.625536	−	0.936180i	0.374424	−	0.927257i	$-0.377840\pi$
$84$	5.83429	+	4.28781i	0.636573	+	0.467838i
$85$	1.46078	+	7.34381i	0.158443	+	0.796548i
$86$	3.59835	−	1.38870i	0.388020	−	0.149748i
$87$	0.0402645	+	9.99977i	0.00431681	+	1.07209i
$88$	−1.93804	+	1.67340i	−0.206596	+	0.178385i
$89$	0.568334	−	0.235412i	0.0602433	−	0.0249536i	−0.352358	−	0.935865i	$-0.614620\pi$
$89$	0.568334	−	0.235412i	0.0602433	−	0.0249536i	0.412602	+	0.910912i	$0.364620\pi$
$90$	−0.0692786	+	4.24208i	−0.00730260	+	0.447154i
$91$	3.45812	+	2.31064i	0.362509	+	0.242221i
$92$	0.198668	−	4.07070i	0.0207126	−	0.424399i
$93$	0.548300	−	0.111361i	0.0568560	−	0.0115476i
$94$	−8.26816	−	5.82111i	−0.852796	−	0.600402i
$95$			0.836395i			0.0858123i
$96$	−4.78816	+	8.54831i	−0.488689	+	0.872458i
$97$			7.81094i			0.793081i	0.918017	+	0.396540i	$0.129789\pi$
$97$			7.81094i			0.793081i	−0.918017	+	0.396540i	$0.870211\pi$
$98$	2.14223	−	3.04277i	0.216398	−	0.307366i
$99$	−2.24592	+	1.52698i	−0.225723	+	0.153467i
$100$	−1.34359	−	1.48147i	−0.134359	−	0.148147i
$101$	−2.47663	−	1.65483i	−0.246434	−	0.164662i	0.426219	−	0.904620i	$-0.359845\pi$
$101$	−2.47663	−	1.65483i	−0.246434	−	0.164662i	−0.672653	+	0.739958i	$0.734845\pi$
$102$	−7.36226	+	16.7985i	−0.728972	+	1.66330i
$103$	−15.7764	+	6.53479i	−1.55449	+	0.643892i	−0.984121	−	0.177496i	$-0.943200\pi$
$103$	−15.7764	+	6.53479i	−1.55449	+	0.643892i	−0.570370	+	0.821388i	$0.693200\pi$
$104$	−2.52804	+	5.02839i	−0.247895	+	0.493074i
$105$	−3.62020	+	0.0145769i	−0.353295	+	0.00142256i
$106$	−1.68975	−	4.37843i	−0.164123	−	0.425270i
$107$	−0.560326	−	2.81695i	−0.0541688	−	0.272325i	0.944203	−	0.329363i	$-0.106834\pi$
$107$	−0.560326	−	2.81695i	−0.0541688	−	0.272325i	−0.998372	+	0.0570388i	$0.981834\pi$
$108$	−6.08670	+	8.42331i	−0.585693	+	0.810533i
$109$	10.1232	+	15.1505i	0.969629	+	1.45115i	0.890869	+	0.454259i	$0.150096\pi$
$109$	10.1232	+	15.1505i	0.969629	+	1.45115i	0.0787600	+	0.996894i	$0.474904\pi$
$110$	0.280306	−	1.24920i	0.0267261	−	0.119106i
$111$	−2.18886	+	5.34515i	−0.207758	+	0.507340i
$112$	−7.37589	−	3.93640i	−0.696956	−	0.371955i
$113$	−8.06111	−	8.06111i	−0.758326	−	0.758326i	0.217692	−	0.976018i	$-0.430147\pi$
$113$	−8.06111	−	8.06111i	−0.758326	−	0.758326i	−0.976018	+	0.217692i	$0.930147\pi$
$114$	−1.17266	+	1.67994i	−0.109829	+	0.157341i
$115$	1.13212	+	1.69434i	0.105571	+	0.157998i
$116$	−1.69795	−	11.4213i	−0.157650	−	1.06044i
$117$	−3.27641	+	4.99002i	−0.302904	+	0.461327i
$118$	−2.90575	−	1.28747i	−0.267496	−	0.118522i
$119$	−14.4590	−	5.98912i	−1.32546	−	0.549022i
$120$	−0.621604	−	4.85938i	−0.0567444	−	0.443599i
$121$	−9.40553	+	3.89590i	−0.855048	+	0.354172i
$122$	−0.490474	+	20.1115i	−0.0444054	+	1.82081i
$123$	−16.3393	−	3.18176i	−1.47327	−	0.286889i
$124$	−0.608213	+	0.217843i	−0.0546191	+	0.0195629i
$125$	0.980785	+	0.195090i	0.0877241	+	0.0174494i
$126$	−7.29181	−	5.04638i	−0.649606	−	0.449567i
$127$		−	4.83808i		−	0.429310i	−0.976690	−	0.214655i	$-0.931137\pi$
$127$		−	4.83808i		−	0.429310i	0.976690	−	0.214655i	$-0.0688628\pi$
$128$	4.05986	−	10.5602i	0.358845	−	0.933397i
$129$	−4.35697	+	1.82530i	−0.383610	+	0.160709i
$130$	−0.481542	−	2.77255i	−0.0422340	−	0.243169i
$131$	−1.13834	+	5.72280i	−0.0994568	+	0.500003i	0.898659	+	0.438648i	$0.144542\pi$
$131$	−1.13834	+	5.72280i	−0.0994568	+	0.500003i	−0.998116	+	0.0613555i	$0.980458\pi$
$132$	2.31443	−	2.11608i	0.201445	−	0.184181i
$133$	−1.45356	−	0.971238i	−0.126040	−	0.0842170i
$134$	0.325422	+	0.00793629i	0.0281122	+	0.000685591i
$135$	−0.0627658	−	5.19577i	−0.00540202	−	0.447181i
$136$	5.63870	−	20.4139i	0.483514	−	1.75048i
$137$	−7.05105	+	17.0228i	−0.602412	+	1.45435i	0.268679	+	0.963230i	$0.413413\pi$
$137$	−7.05105	+	17.0228i	−0.602412	+	1.45435i	−0.871091	+	0.491122i	$0.836587\pi$
$138$	−0.101602	+	4.99046i	−0.00864891	+	0.424816i
$139$	4.39734	+	22.1069i	0.372978	+	1.87509i	0.474506	+	0.880252i	$0.342627\pi$
$139$	4.39734	+	22.1069i	0.372978	+	1.87509i	−0.101528	+	0.994833i	$0.532373\pi$
$140$	4.13484	−	0.614704i	0.349458	−	0.0519520i
$141$	10.3248	+	6.83885i	0.869507	+	0.575935i
$142$	2.04790	−	1.29728i	0.171856	−	0.108865i
$143$	1.27376	−	1.27376i	0.106517	−	0.106517i
$144$	5.56452	−	10.6318i	0.463710	−	0.885987i
$145$	4.08242	+	4.08242i	0.339027	+	0.339027i
$146$	2.52925	+	0.567536i	0.209323	+	0.0469696i
$147$	−2.51677	+	3.79964i	−0.207580	+	0.313389i
$148$	1.61848	−	6.47016i	0.133038	−	0.531844i
$149$	−4.85645	+	0.966008i	−0.397856	+	0.0791385i	−0.389963	−	0.920830i	$-0.627512\pi$
$149$	−4.85645	+	0.966008i	−0.397856	+	0.0791385i	−0.00789269	+	0.999969i	$0.502512\pi$
$150$	1.69644	+	1.76695i	0.138513	+	0.144271i
$151$	−6.92496	−	2.86841i	−0.563545	−	0.233428i	0.0826781	−	0.996576i	$-0.473653\pi$
$151$	−6.92496	−	2.86841i	−0.563545	−	0.233428i	−0.646224	+	0.763148i	$0.723653\pi$
$152$	1.06262	−	2.11360i	0.0861897	−	0.171435i
$153$	8.42884	−	20.8217i	0.681431	−	1.68334i
$154$	1.84547	+	1.93773i	0.148712	+	0.156147i
$155$	0.179463	−	0.268585i	0.0144148	−	0.0215732i
$156$	2.92002	−	6.24396i	0.233788	−	0.499917i
$157$	6.34758	+	1.26261i	0.506592	+	0.100767i	0.441768	−	0.897129i	$-0.354351\pi$
$157$	6.34758	+	1.26261i	0.506592	+	0.100767i	0.0648240	+	0.997897i	$0.479351\pi$
$158$	4.67834	+	3.29373i	0.372189	+	0.262035i
$159$	2.22101	+	5.30150i	0.176137	+	0.420437i
$160$	1.51314	+	5.45073i	0.119624	+	0.430918i
$161$	−4.25923			−0.335674
$162$	7.15860	−	10.5240i	0.562433	−	0.826843i
$163$	3.97072	−	19.9622i	0.311011	−	1.56356i	−0.436747	−	0.899585i	$-0.643869\pi$
$163$	3.97072	−	19.9622i	0.311011	−	1.56356i	0.747757	−	0.663972i	$-0.231131\pi$
$164$	19.1986	+	0.936976i	1.49916	+	0.0731655i
$165$	−0.299705	+	1.53908i	−0.0233320	+	0.119817i
$166$	−10.0046	−	10.5048i	−0.776509	−	0.815330i
$167$	7.10453	+	17.1519i	0.549765	+	1.32725i	0.917654	+	0.397381i	$0.130081\pi$
$167$	7.10453	+	17.1519i	0.549765	+	1.32725i	−0.367889	+	0.929870i	$0.619919\pi$
$168$	9.16689	+	4.56253i	0.707241	+	0.352007i
$169$	−3.45967	+	8.35237i	−0.266128	+	0.642490i
$170$	3.81259	+	9.87902i	0.292412	+	0.757687i
$171$	1.37718	−	2.09747i	0.105316	−	0.160397i
$172$	4.67771	−	2.80576i	0.356672	−	0.213937i
$173$	1.16476	−	0.778269i	0.0885552	−	0.0591707i	−0.510504	−	0.859875i	$-0.670541\pi$
$173$	1.16476	−	0.778269i	0.0885552	−	0.0591707i	0.599060	+	0.800704i	$0.295541\pi$
$174$	2.47605	+	13.9235i	0.187709	+	1.05554i
$175$	−1.47795	+	1.47795i	−0.111723	+	0.111723i
$176$	−2.29541	+	2.80064i	−0.173023	+	0.211106i
$177$	3.60216	+	1.47510i	0.270755	+	0.110875i
$178$	0.734921	−	0.465549i	0.0550846	−	0.0348944i
$179$	−15.9651	+	10.6676i	−1.19329	+	0.797331i	−0.983587	−	0.180434i	$-0.942250\pi$
$179$	−15.9651	+	10.6676i	−1.19329	+	0.797331i	−0.209703	+	0.977765i	$0.567250\pi$
$180$	0.930055	+	5.92748i	0.0693222	+	0.441808i
$181$	−12.7121	+	2.52860i	−0.944884	+	0.187949i	−0.643407	−	0.765524i	$-0.722480\pi$
$181$	−12.7121	+	2.52860i	−0.944884	+	0.187949i	−0.301477	+	0.953473i	$0.597480\pi$
$182$	5.37756	+	2.38267i	0.398611	+	0.176615i
$183$	−0.0992083	−	24.6386i	−0.00733369	−	1.82134i
$184$	−0.708296	−	5.72000i	−0.0522163	−	0.421684i
$185$	1.27616	+	3.08091i	0.0938248	+	0.226513i
$186$	0.737026	−	0.287854i	0.0540414	−	0.0211065i
$187$	−3.76591	+	5.63608i	−0.275391	+	0.412151i
$188$	−12.9292	−	6.10996i	−0.942958	−	0.445615i
$189$	9.10256	+	5.92436i	0.662114	+	0.430933i
$190$	0.202408	+	1.16539i	0.0146842	+	0.0845466i
$191$	24.4677			1.77042			0.885209	−	0.465193i	$-0.154015\pi$
$191$	24.4677			1.77042			0.885209	+	0.465193i	$0.154015\pi$
$192$	−4.60291	+	13.0696i	−0.332186	+	0.943214i
$193$	15.6475			1.12633			0.563166	−	0.826344i	$-0.309583\pi$
$193$	15.6475			1.12633			0.563166	+	0.826344i	$0.309583\pi$
$194$	1.89025	+	10.8834i	0.135712	+	0.781383i
$195$	0.685984	+	3.37754i	0.0491244	+	0.241871i
$196$	2.24853	−	4.75808i	0.160609	−	0.339863i
$197$	3.63117	−	5.43443i	0.258710	−	0.387187i	−0.679263	−	0.733895i	$-0.737701\pi$
$197$	3.63117	−	5.43443i	0.258710	−	0.387187i	0.937973	+	0.346708i	$0.112701\pi$
$198$	−2.75983	+	2.67113i	−0.196132	+	0.189829i
$199$	−1.83103	−	4.42049i	−0.129798	−	0.313360i	0.845598	−	0.533820i	$-0.179244\pi$
$199$	−1.83103	−	4.42049i	−0.129798	−	0.313360i	−0.975396	+	0.220460i	$0.929244\pi$
$200$	−2.23062	−	1.73906i	−0.157729	−	0.122970i
$201$	−0.398674	+	0.00160528i	−0.0281203	+	0.000113228i
$202$	−3.85130	−	1.70642i	−0.270976	−	0.120063i
$203$	−11.8354	+	2.35420i	−0.830681	+	0.165233i
$204$	−6.19299	+	25.1879i	−0.433596	+	1.76351i
$205$	−7.99101	+	5.33942i	−0.558117	+	0.372922i
$206$	−20.4006	+	12.9232i	−1.42138	+	0.900399i
$207$	−0.0492302	−	6.11311i	−0.00342174	−	0.424891i
$208$	−2.30558	+	7.61811i	−0.159863	+	0.528221i
$209$	−0.535401	+	0.535401i	−0.0370345	+	0.0370345i
$210$	−5.04069	+	0.896402i	−0.347841	+	0.0618576i
$211$	2.85775	−	1.90949i	0.196735	−	0.131454i	−0.453301	−	0.891358i	$-0.649754\pi$
$211$	2.85775	−	1.90949i	0.196735	−	0.131454i	0.650036	+	0.759903i	$0.274754\pi$
$212$	−3.41401	−	5.69178i	−0.234475	−	0.390913i
$213$	−2.46201	+	1.65944i	−0.168694	+	0.113703i
$214$	−1.46244	−	3.78941i	−0.0999701	−	0.259039i
$215$	−1.04370	+	2.51972i	−0.0711799	+	0.171844i
$216$	−6.44248	+	13.2096i	−0.438355	+	0.898802i
$217$	0.258375	+	0.623772i	0.0175396	+	0.0423444i
$218$	17.7717	+	18.6602i	1.20365	+	1.26383i
$219$	−3.11619	−	0.606815i	−0.210572	−	0.0410047i
$220$	0.0882584	−	1.80841i	0.00595038	−	0.121923i
$221$	−2.90671	+	14.6130i	−0.195526	+	0.982977i
$222$	−1.75633	+	7.97740i	−0.117877	+	0.535408i
$223$	−23.3025			−1.56045			−0.780226	−	0.625497i	$-0.784896\pi$
$223$	−23.3025			−1.56045			−0.780226	+	0.625497i	$0.784896\pi$
$224$	−11.2298	−	3.69983i	−0.750325	−	0.247205i
$225$	−2.13833	−	2.10417i	−0.142556	−	0.140278i
$226$	−13.1828	−	9.28119i	−0.876905	−	0.617375i
$227$	16.4613	+	3.27435i	1.09257	+	0.217327i	0.708313	−	0.705898i	$-0.249456\pi$
$227$	16.4613	+	3.27435i	1.09257	+	0.217327i	0.384261	+	0.923225i	$0.374456\pi$
$228$	−1.22738	+	2.62454i	−0.0812852	+	0.173814i
$229$	8.97503	−	13.4321i	0.593087	−	0.887617i	−0.406575	−	0.913617i	$-0.633277\pi$
$229$	8.97503	−	13.4321i	0.593087	−	0.887617i	0.999662	+	0.0260004i	$0.00827713\pi$
$230$	1.98748	+	2.08685i	0.131051	+	0.137603i
$231$	−2.32673	−	2.30807i	−0.153088	−	0.151860i
$232$	−5.12980	−	15.5030i	−0.336788	−	1.01782i
$233$	13.0296	+	5.39704i	0.853598	+	0.353572i	0.766201	−	0.642602i	$-0.222145\pi$
$233$	13.0296	+	5.39704i	0.853598	+	0.353572i	0.0873976	+	0.996174i	$0.472145\pi$
$234$	−3.35761	+	7.74575i	−0.219494	+	0.506356i
$235$	7.01271	−	1.39492i	0.457459	−	0.0909942i
$236$	−4.36031	−	1.09071i	−0.283832	−	0.0709993i
$237$	−5.84205	−	3.86960i	−0.379482	−	0.251357i
$238$	−21.5959	−	4.84587i	−1.39985	−	0.314111i
$239$	−6.31391	−	6.31391i	−0.408413	−	0.408413i	0.472772	−	0.881185i	$-0.343253\pi$
$239$	−6.31391	−	6.31391i	−0.408413	−	0.408413i	−0.881185	+	0.472772i	$0.843253\pi$
$240$	−2.04209	−	6.62041i	−0.131816	−	0.427346i
$241$	−1.69145	+	1.69145i	−0.108956	+	0.108956i	−0.759483	−	0.650527i	$-0.774548\pi$
$241$	−1.69145	+	1.69145i	−0.108956	+	0.108956i	0.650527	+	0.759483i	$0.274548\pi$
$242$	−12.1624	+	7.70451i	−0.781830	+	0.495264i
$243$	−8.39780	+	13.1330i	−0.538719	+	0.842485i
$244$	4.18359	+	28.1411i	0.267827	+	1.80155i
$245$	0.513344	+	2.58075i	0.0327963	+	0.164878i
$246$	−23.5365	−	0.479183i	−1.50063	−	0.0305516i
$247$	−0.636896	+	1.53760i	−0.0405247	+	0.0978354i
$248$	−0.794738	+	0.450720i	−0.0504659	+	0.0286208i
$249$	12.6136	+	12.5124i	0.799355	+	0.792944i
$250$	1.41379	+	0.0344792i	0.0894161	+	0.00218066i
$251$	15.6054	+	10.4272i	0.985003	+	0.658158i	0.940123	−	0.340834i	$-0.110709\pi$
$251$	15.6054	+	10.4272i	0.985003	+	0.658158i	0.0448799	+	0.998992i	$0.485709\pi$
$252$	−11.3813	−	5.26677i	−0.716954	−	0.331776i
$253$	−0.359894	+	1.80931i	−0.0226263	+	0.113750i
$254$	−1.17082	−	6.74116i	−0.0734637	−	0.422978i
$255$	−5.01125	−	11.9618i	−0.313816	−	0.749075i
$256$	3.10126	−	15.6966i	0.193828	−	0.981035i
$257$		−	26.0836i		−	1.62705i	−0.581532	−	0.813524i	$-0.697546\pi$
$257$		−	26.0836i		−	1.62705i	0.581532	−	0.813524i	$-0.302454\pi$
$258$	−5.62908	+	3.59768i	−0.350451	+	0.223982i
$259$	−6.83618	−	1.35980i	−0.424780	−	0.0844939i
$260$	−1.34192	−	3.74661i	−0.0832222	−	0.232355i
$261$	−3.51570	−	16.9597i	−0.217617	−	1.04978i
$262$	−0.201183	+	8.24936i	−0.0124291	+	0.509647i
$263$	−12.3008	+	5.09515i	−0.758498	+	0.314180i	−0.728204	−	0.685361i	$-0.759644\pi$
$263$	−12.3008	+	5.09515i	−0.758498	+	0.314180i	−0.0302945	+	0.999541i	$0.509644\pi$
$264$	2.71273	−	3.50854i	0.166957	−	0.215936i
$265$	3.06596	+	1.26996i	0.188341	+	0.0780132i
$266$	−2.26036	−	1.00152i	−0.138592	−	0.0614069i
$267$	−0.883531	+	0.595516i	−0.0540712	+	0.0364450i
$268$	0.455348	−	0.0676942i	0.0278148	−	0.00413508i
$269$	2.86120	+	4.28208i	0.174450	+	0.261083i	0.908383	−	0.418139i	$-0.137317\pi$
$269$	2.86120	+	4.28208i	0.174450	+	0.261083i	−0.733933	+	0.679222i	$0.762317\pi$
$270$	−1.34484	−	7.22436i	−0.0818441	−	0.439661i
$271$	5.19243	+	5.19243i	0.315418	+	0.315418i	0.847004	−	0.531586i	$-0.178404\pi$
$271$	5.19243	+	5.19243i	0.315418	+	0.315418i	−0.531586	+	0.847004i	$0.678404\pi$
$272$	2.91651	−	29.8084i	0.176840	−	1.80740i
$273$	−6.66637	−	2.72991i	−0.403467	−	0.165221i
$274$	−5.70510	+	25.4251i	−0.344658	+	1.53599i
$275$	0.502947	+	0.752713i	0.0303288	+	0.0453903i
$276$	1.06613	+	6.97807i	0.0641734	+	0.420030i
$277$	3.83013	+	19.2553i	0.230130	+	1.15694i	0.907095	+	0.420926i	$0.138295\pi$
$277$	3.83013	+	19.2553i	0.230130	+	1.15694i	−0.676965	+	0.736015i	$0.736705\pi$
$278$	11.4769	+	29.7386i	0.688341	+	1.78360i
$279$	−0.892291	+	0.378046i	−0.0534201	+	0.0226330i
$280$	5.61254	−	1.85713i	0.335413	−	0.110985i
$281$	25.1193	−	10.4047i	1.49849	−	0.620695i	0.525346	−	0.850889i	$-0.323936\pi$
$281$	25.1193	−	10.4047i	1.49849	−	0.620695i	0.973145	+	0.230193i	$0.0739358\pi$
$282$	16.0411	+	7.03033i	0.955236	+	0.418650i
$283$	19.2759	+	12.8797i	1.14583	+	0.765621i	0.975551	−	0.219775i	$-0.0705323\pi$
$283$	19.2759	+	12.8797i	1.14583	+	0.765621i	0.170282	+	0.985395i	$0.445532\pi$
$284$	2.53950	−	2.30316i	0.150692	−	0.136667i
$285$	−0.288342	−	1.41969i	−0.0170799	−	0.0840953i
$286$	1.46654	−	2.08304i	0.0867185	−	0.123173i
$287$		−	20.0877i		−	1.18574i
$288$	5.18043	−	16.1605i	0.305260	−	0.952269i
$289$		−	39.0655i		−	2.29797i
$290$	6.67621	+	4.70031i	0.392040	+	0.276012i
$291$	−2.69277	−	13.2583i	−0.157853	−	0.777213i
$292$	3.66149	+	0.178697i	0.214273	+	0.0104575i
$293$	−7.42414	−	4.96065i	−0.433723	−	0.289805i	0.319479	−	0.947593i	$-0.396492\pi$
$293$	−7.42414	−	4.96065i	−0.433723	−	0.289805i	−0.753203	+	0.657789i	$0.771492\pi$
$294$	−2.58723	+	5.90331i	−0.150891	+	0.344288i
$295$	2.07626	−	0.860017i	0.120885	−	0.0500721i
$296$	0.689331	−	9.40689i	0.0400666	−	0.546764i
$297$	3.28579	−	3.36615i	0.190661	−	0.195324i
$298$	−6.53298	+	2.52126i	−0.378446	+	0.146052i
$299$	0.791059	+	3.97692i	0.0457481	+	0.229991i
$300$	2.79134	+	2.05145i	0.161158	+	0.118440i
$301$	−3.16703	−	4.73979i	−0.182544	−	0.273197i
$302$	−10.3431	−	2.32087i	−0.595178	−	0.133551i
$303$	4.77432	+	1.95510i	0.274278	+	0.112318i
$304$	0.969111	−	3.20214i	0.0555823	−	0.183655i
$305$	−10.0587	−	10.0587i	−0.575962	−	0.575962i
$306$	6.70549	−	31.0518i	0.383327	−	1.77511i
$307$	12.9921	+	19.4440i	0.741495	+	1.10973i	0.989996	+	0.141095i	$0.0450622\pi$
$307$	12.9921	+	19.4440i	0.741495	+	1.10973i	−0.248501	+	0.968632i	$0.579938\pi$
$308$	3.04033	+	2.25334i	0.173239	+	0.128396i
$309$	24.5259	−	16.5309i	1.39523	−	0.940411i
$310$	0.185057	−	0.417664i	0.0105105	−	0.0237217i
$311$	14.7662	+	6.11637i	0.837316	+	0.346828i	0.759795	−	0.650163i	$-0.225299\pi$
$311$	14.7662	+	6.11637i	0.837316	+	0.346828i	0.0775213	+	0.996991i	$0.475299\pi$
$312$	2.55758	−	9.40669i	0.144794	−	0.532549i
$313$	11.3587	−	4.70494i	0.642034	−	0.265939i	−0.0378224	−	0.999284i	$-0.512042\pi$
$313$	11.3587	−	4.70494i	0.642034	−	0.265939i	0.679856	+	0.733345i	$0.262042\pi$
$314$	9.14998	+	0.223147i	0.516363	+	0.0125929i
$315$	6.13989	−	1.27278i	0.345943	−	0.0717133i
$316$	7.31567	+	3.45718i	0.411539	+	0.194481i
$317$	−16.9461	−	3.37078i	−0.951785	−	0.189322i	−0.305307	−	0.952254i	$-0.598759\pi$
$317$	−16.9461	−	3.37078i	−0.951785	−	0.189322i	−0.646479	+	0.762932i	$0.723759\pi$
$318$	4.37762	+	6.84939i	0.245484	+	0.384095i
$319$			5.22656i			0.292631i
$320$	3.42742	+	7.22861i	0.191598	+	0.404092i
$321$	1.92222	+	4.58831i	0.107288	+	0.256094i
$322$	−5.93461	+	1.03074i	−0.330723	+	0.0574407i
$323$	1.22178	−	6.14233i	0.0679819	−	0.341768i
$324$	7.42766	−	16.3960i	0.412648	−	0.910891i
$325$	1.65449	+	1.10549i	0.0917746	+	0.0613218i
$326$	0.701763	−	28.7753i	0.0388671	−	1.59371i
$327$	−22.4062	−	22.2264i	−1.23906	−	1.22913i
$328$	26.9772	−	3.34053i	1.48956	−	0.184450i
$329$	−5.71909	+	13.8071i	−0.315304	+	0.761211i
$330$	−0.0451366	+	2.21702i	−0.00248469	+	0.122043i
$331$	−4.79546	−	24.1084i	−0.263582	−	1.32512i	−0.854948	−	0.518714i	$-0.826411\pi$
$331$	−4.79546	−	24.1084i	−0.263582	−	1.32512i	0.591365	−	0.806404i	$-0.298589\pi$
$332$	−16.4821	−	12.2158i	−0.904575	−	0.670428i
$333$	1.87266	−	9.82744i	0.102621	−	0.538540i
$334$	14.0499	+	22.1793i	0.768776	+	1.21360i
$335$	−0.162759	+	0.162759i	−0.00889249	+	0.00889249i
$336$	13.8769	+	4.13883i	0.757044	+	0.225792i
$337$	−9.10320	−	9.10320i	−0.495883	−	0.495883i	0.414271	−	0.910154i	$-0.364037\pi$
$337$	−9.10320	−	9.10320i	−0.495883	−	0.495883i	−0.910154	+	0.414271i	$0.864037\pi$
$338$	−2.79926	+	12.4751i	−0.152260	+	0.678554i
$339$	16.4619	+	10.9039i	0.894088	+	0.592217i
$340$	7.70301	+	12.8423i	0.417754	+	0.696473i
$341$	0.286809	−	0.0570498i	0.0155316	−	0.00308942i
$342$	1.41131	−	3.25580i	0.0763151	−	0.176053i
$343$	−18.5984	−	7.70372i	−1.00422	−	0.415962i
$344$	5.83871	−	5.04142i	0.314802	−	0.271815i
$345$	−2.50578	−	2.48568i	−0.134907	−	0.133824i
$346$	1.43458	−	1.36628i	0.0771237	−	0.0734515i
$347$	9.17754	−	13.7352i	0.492676	−	0.737342i	−0.498929	−	0.866643i	$-0.666273\pi$
$347$	9.17754	−	13.7352i	0.492676	−	0.737342i	0.991605	+	0.129301i	$0.0412733\pi$
$348$	6.81951	+	18.8011i	0.365564	+	1.00785i
$349$	−23.8817	−	4.75037i	−1.27836	−	0.254281i	−0.491208	−	0.871042i	$-0.663444\pi$
$349$	−23.8817	−	4.75037i	−1.27836	−	0.254281i	−0.787150	+	0.616761i	$0.788444\pi$
$350$	−1.70165	+	2.41698i	−0.0909568	+	0.129193i
$351$	3.84108	−	9.59955i	0.205022	−	0.512386i
$352$	−2.52057	+	4.45778i	−0.134347	+	0.237600i
$353$	−9.23012			−0.491270			−0.245635	−	0.969362i	$-0.578996\pi$
$353$	−9.23012			−0.491270			−0.245635	+	0.969362i	$0.578996\pi$
$354$	5.37606	+	1.18361i	0.285735	+	0.0629082i
$355$	−0.334419	+	1.68124i	−0.0177491	+	0.0892309i
$356$	0.911342	−	0.826526i	0.0483010	−	0.0438058i
$357$	26.6074	+	5.18125i	1.40821	+	0.274221i
$358$	−19.6635	+	18.7273i	−1.03925	+	0.989767i
$359$	−4.50319	−	10.8717i	−0.237670	−	0.573785i	0.759371	−	0.650657i	$-0.225507\pi$
$359$	−4.50319	−	10.8717i	−0.237670	−	0.573785i	−0.997041	+	0.0768724i	$0.975507\pi$
$360$	2.73035	+	8.03400i	0.143902	+	0.423429i
$361$	−7.00328	+	16.9074i	−0.368594	+	0.889863i
$362$	−17.1006	+	6.59957i	−0.898785	+	0.346866i
$363$	14.6218	−	9.85537i	0.767446	−	0.517273i
$364$	8.06945	+	2.01853i	0.422954	+	0.105800i
$365$	−1.52402	+	1.01832i	−0.0797709	+	0.0533012i
$366$	−6.10079	−	34.3063i	−0.318893	−	1.79322i
$367$	−12.3817	+	12.3817i	−0.646318	+	0.646318i	−0.952101	−	0.305783i	$-0.901082\pi$
$367$	−12.3817	+	12.3817i	−0.646318	+	0.646318i	0.305783	+	0.952101i	$0.401082\pi$
$368$	−2.37115	−	7.79857i	−0.123605	−	0.406529i
$369$	28.8312	−	0.232184i	1.50089	−	0.0120870i
$370$	2.52372	+	3.98397i	0.131202	+	0.207117i
$371$	−5.76731	+	3.85359i	−0.299424	+	0.200069i
$372$	0.957278	−	0.579443i	0.0496326	−	0.0300427i
$373$	−26.5868	+	5.28845i	−1.37661	+	0.273826i	−0.827286	−	0.561781i	$-0.810116\pi$
$373$	−26.5868	+	5.28845i	−1.37661	+	0.273826i	−0.549329	+	0.835606i	$0.685116\pi$
$374$	−3.88331	+	8.76441i	−0.200801	+	0.453197i
$375$	−1.73204	+	0.00697412i	−0.0894420	+	0.000360142i
$376$	−19.4936	−	5.38447i	−1.00530	−	0.277683i
$377$	4.39633	+	10.6137i	0.226423	+	0.546632i
$378$	14.1168	+	6.05190i	0.726089	+	0.311276i
$379$	1.20989	−	1.81073i	0.0621481	−	0.0930112i	−0.799094	−	0.601206i	$-0.794687\pi$
$379$	1.20989	−	1.81073i	0.0621481	−	0.0930112i	0.861242	+	0.508195i	$0.169687\pi$
$380$	0.564052	+	1.57482i	0.0289353	+	0.0807867i
$381$	1.66790	+	8.21214i	0.0854490	+	0.420721i
$382$	34.0921	−	5.92119i	1.74431	−	0.302955i
$383$	34.3779			1.75663			0.878314	−	0.478084i	$-0.158669\pi$
$383$	34.3779			1.75663			0.878314	+	0.478084i	$0.158669\pi$
$384$	−3.25064	+	19.3244i	−0.165883	+	0.986145i
$385$	−1.89216			−0.0964336
$386$	21.8025	−	3.78671i	1.10972	−	0.192738i
$387$	6.76624	−	4.60030i	0.343947	−	0.233846i
$388$	5.26758	+	14.7070i	0.267421	+	0.746634i
$389$	21.3730	−	31.9870i	1.08366	−	1.62181i	0.358040	−	0.933706i	$-0.383445\pi$
$389$	21.3730	−	31.9870i	1.08366	−	1.62181i	0.725616	−	0.688100i	$-0.241555\pi$
$390$	1.77319	+	4.54010i	0.0897888	+	0.229897i
$391$	−5.83906	−	14.0967i	−0.295294	−	0.712902i
$392$	1.98154	−	7.17384i	0.100083	−	0.362333i
$393$	−0.0406934	−	10.1063i	−0.00205271	−	0.509795i
$394$	3.74437	−	8.45083i	0.188639	−	0.425746i
$395$	−3.96797	+	0.789279i	−0.199650	+	0.0397129i
$396$	−3.19900	+	4.38971i	−0.160756	+	0.220591i
$397$	−18.0537	+	12.0631i	−0.906089	+	0.605430i	−0.918901	−	0.394488i	$-0.870922\pi$
$397$	−18.0537	+	12.0631i	−0.906089	+	0.605430i	0.0128115	+	0.999918i	$0.495922\pi$
$398$	−3.62103	−	5.71620i	−0.181506	−	0.286527i
$399$	2.80210	+	1.14747i	0.140280	+	0.0574453i
$400$	−3.52890	−	1.88332i	−0.176445	−	0.0941659i
$401$	−0.760384	+	0.760384i	−0.0379717	+	0.0379717i	−0.725838	−	0.687866i	$-0.758548\pi$
$401$	−0.760384	+	0.760384i	−0.0379717	+	0.0379717i	0.687866	+	0.725838i	$0.258548\pi$
$402$	−0.555105	+	0.0987161i	−0.0276861	+	0.00492351i
$403$	0.534440	−	0.357102i	0.0266224	−	0.0177885i
$404$	−5.77918	−	1.44563i	−0.287525	−	0.0719230i
$405$	1.89775	+	8.79764i	0.0942999	+	0.437158i
$406$	−15.9212	+	6.14441i	−0.790154	+	0.304942i
$407$	−1.15528	+	2.78909i	−0.0572651	+	0.138250i
$408$	−2.53352	+	36.5944i	−0.125428	+	1.81169i
$409$	−9.87612	−	23.8431i	−0.488343	−	1.17896i	−0.955553	−	0.294818i	$-0.904741\pi$
$409$	−9.87612	−	23.8431i	−0.488343	−	1.17896i	0.467211	−	0.884146i	$-0.345259\pi$
$410$	−9.84217	+	9.37354i	−0.486070	+	0.462926i
$411$	6.09994	−	31.3251i	0.300888	−	1.54516i
$412$	−25.2979	+	22.9435i	−1.24634	+	1.13035i
$413$	−0.916386	+	4.60698i	−0.0450924	+	0.226695i
$414$	−1.54797	−	8.50582i	−0.0760787	−	0.418038i
$415$	10.2578			0.503533
$416$	−1.36890	+	11.1727i	−0.0671158	+	0.547786i
$417$	−15.0853	−	36.0082i	−0.738728	−	1.76333i
$418$	−0.616436	+	0.875571i	−0.0301509	+	0.0428256i
$419$	−3.15647	−	0.627861i	−0.154204	−	0.0306730i	0.117385	−	0.993087i	$-0.462549\pi$
$419$	−3.15647	−	0.627861i	−0.154204	−	0.0306730i	−0.271588	+	0.962414i	$0.587549\pi$
$420$	−6.80654	+	2.46886i	−0.332125	+	0.120468i
$421$	−4.23976	+	6.34525i	−0.206633	+	0.309249i	−0.920282	−	0.391255i	$-0.872041\pi$
$421$	−4.23976	+	6.34525i	−0.206633	+	0.309249i	0.713649	+	0.700503i	$0.247041\pi$
$422$	3.51976	−	3.35217i	0.171339	−	0.163181i
$423$	−19.8830	−	8.04882i	−0.966742	−	0.391347i
$424$	−6.13433	−	7.10447i	−0.297910	−	0.345023i
$425$	−6.91772	−	2.86541i	−0.335559	−	0.138993i
$426$	−3.02886	+	2.90799i	−0.146749	+	0.140893i
$427$	29.1614	−	5.80056i	1.41122	−	0.280709i
$428$	−2.95473	−	4.92608i	−0.142822	−	0.238111i
$429$	−1.72295	+	2.60119i	−0.0831847	+	0.125586i
$430$	−0.844473	+	3.76344i	−0.0407241	+	0.181489i
$431$	20.8768	+	20.8768i	1.00560	+	1.00560i	0.999984	+	0.00561382i	$0.00178694\pi$
$431$	20.8768	+	20.8768i	1.00560	+	1.00560i	0.00561382	+	0.999984i	$0.498213\pi$
$432$	−5.77992	+	19.9648i	−0.278087	+	0.960556i
$433$	20.7804	−	20.7804i	0.998644	−	0.998644i	−0.00135483	−	0.999999i	$-0.500431\pi$
$433$	20.7804	−	20.7804i	0.998644	−	0.998644i	0.999999	+	0.00135483i	$0.000431256\pi$
$434$	0.510961	+	0.806608i	0.0245269	+	0.0387184i
$435$	−8.33687	−	5.52210i	−0.399723	−	0.264764i
$436$	29.2780	+	21.6995i	1.40216	+	1.03922i
$437$	−0.332508	−	1.67163i	−0.0159060	−	0.0799649i
$438$	−4.48880	−	0.0913883i	−0.214483	−	0.00436670i
$439$	−7.28373	+	17.5845i	−0.347634	+	0.839262i	0.649265	+	0.760562i	$0.275077\pi$
$439$	−7.28373	+	17.5845i	−0.347634	+	0.839262i	−0.996898	+	0.0786993i	$0.974923\pi$
$440$	−0.314661	−	2.54111i	−0.0150009	−	0.121143i
$441$	2.96205	−	7.31714i	0.141050	−	0.348435i
$442$	−0.513715	+	21.0645i	−0.0244350	+	1.00194i
$443$	6.19587	+	4.13995i	0.294375	+	0.196695i	0.693984	−	0.719991i	$-0.255854\pi$
$443$	6.19587	+	4.13995i	0.294375	+	0.196695i	−0.399609	+	0.916686i	$0.630854\pi$
$444$	−0.516653	+	11.5404i	−0.0245192	+	0.547682i
$445$	−0.120012	+	0.603340i	−0.00568911	+	0.0286011i
$446$	−32.4687	+	5.63923i	−1.53744	+	0.267025i
$447$	7.91030	−	3.31393i	0.374144	−	0.156744i
$448$	−16.5425	−	2.43754i	−0.781560	−	0.115163i
$449$			1.05967i			0.0500091i	0.999687	+	0.0250045i	$0.00796003\pi$
$449$			1.05967i			0.0500091i	−0.999687	+	0.0250045i	$0.992040\pi$
$450$	−3.48867	−	2.41437i	−0.164457	−	0.113815i
$451$	−8.53321	−	1.69736i	−0.401813	−	0.0799256i
$452$	−20.6143	−	9.74174i	−0.969617	−	0.458213i
$453$	12.7433	+	2.48149i	0.598731	+	0.116591i
$454$	23.7288	+	0.578691i	1.11365	+	0.0271593i
$455$	−3.84245	+	1.59160i	−0.180137	+	0.0746152i
$456$	−1.07503	+	3.95394i	−0.0503430	+	0.185160i
$457$	−1.60022	−	0.662832i	−0.0748551	−	0.0310060i	0.344942	−	0.938624i	$-0.387899\pi$
$457$	−1.60022	−	0.662832i	−0.0748551	−	0.0310060i	−0.419797	+	0.907618i	$0.637899\pi$
$458$	9.25482	−	20.8876i	0.432449	−	0.976014i
$459$	−7.12892	+	38.2485i	−0.332749	+	1.78529i
$460$	3.27429	+	2.42674i	0.152664	+	0.113148i
$461$	5.83098	+	8.72668i	0.271576	+	0.406442i	0.942040	−	0.335500i	$-0.108905\pi$
$461$	5.83098	+	8.72668i	0.271576	+	0.406442i	−0.670464	+	0.741942i	$0.733905\pi$
$462$	−3.80051	−	2.65289i	−0.176816	−	0.123423i
$463$	26.8517	+	26.8517i	1.24791	+	1.24791i	0.956643	+	0.291262i	$0.0940752\pi$
$463$	26.8517	+	26.8517i	1.24791	+	1.24791i	0.291262	+	0.956643i	$0.405925\pi$
$464$	−10.8994	−	20.3598i	−0.505991	−	0.945179i
$465$	−0.212026	+	0.517763i	−0.00983248	+	0.0240107i
$466$	19.4609	+	4.36682i	0.901511	+	0.202289i
$467$	5.71941	+	8.55970i	0.264663	+	0.396096i	0.939870	−	0.341532i	$-0.110946\pi$
$467$	5.71941	+	8.55970i	0.264663	+	0.396096i	−0.675207	+	0.737628i	$0.735946\pi$
$468$	−2.80386	+	11.6051i	−0.129608	+	0.536447i
$469$	−0.0938581	−	0.471857i	−0.00433396	−	0.0217883i
$470$	9.43362	−	3.64069i	0.435140	−	0.167933i
$471$	−11.2096	+	0.0451361i	−0.516513	+	0.00207976i
$472$	−6.33942	−	0.464549i	−0.291795	−	0.0213826i
$473$	−2.28105	+	0.944844i	−0.104883	+	0.0434440i
$474$	−9.07649	−	3.97794i	−0.416897	−	0.182713i
$475$	−0.695437	−	0.464676i	−0.0319088	−	0.0213208i
$476$	−31.2634	−	1.52580i	−1.43296	−	0.0699347i
$477$	−5.59759	−	8.23307i	−0.256296	−	0.376966i
$478$	−10.3255	−	7.26954i	−0.472276	−	0.332501i
$479$		−	30.1362i		−	1.37696i	−0.725257	−	0.688478i	$-0.758279\pi$
$479$		−	30.1362i		−	1.37696i	0.725257	−	0.688478i	$-0.241721\pi$
$480$	−4.44750	−	8.73039i	−0.203000	−	0.398486i
$481$			6.63563i			0.302558i
$482$	−1.94746	+	2.76612i	−0.0887043	+	0.125993i
$483$	7.22959	−	1.46834i	0.328958	−	0.0668119i
$484$	−15.0821	+	13.6784i	−0.685548	+	0.621746i
$485$	−6.49456	−	4.33952i	−0.294903	−	0.197048i
$486$	−8.52290	+	20.3313i	−0.386607	+	0.922245i
$487$	−22.3962	+	9.27683i	−1.01487	+	0.420373i	−0.827229	−	0.561865i	$-0.810084\pi$
$487$	−22.3962	+	9.27683i	−1.01487	+	0.420373i	−0.187641	+	0.982238i	$0.560084\pi$
$488$	12.6394	+	38.1981i	0.572159	+	1.72915i
$489$	0.141946	+	35.2526i	0.00641902	+	1.59418i
$490$	1.33981	+	3.47167i	0.0605266	+	0.156834i
$491$	2.86724	+	14.4146i	0.129397	+	0.650522i	0.989979	+	0.141211i	$0.0450997\pi$
$491$	2.86724	+	14.4146i	0.129397	+	0.650522i	−0.860583	+	0.509311i	$0.829900\pi$
$492$	−32.9106	+	5.02817i	−1.48372	+	0.226687i
$493$	−24.0170	−	35.9440i	−1.08167	−	1.61884i
$494$	−0.515321	+	2.29656i	−0.0231854	+	0.103327i
$495$	−0.0218706	−	2.71575i	−0.000983009	−	0.122064i
$496$	−0.998277	+	0.820340i	−0.0448240	+	0.0368343i
$497$	−2.53347	−	2.53347i	−0.113642	−	0.113642i
$498$	20.6032	+	14.3818i	0.923254	+	0.644462i
$499$	10.3694	+	15.5190i	0.464200	+	0.694724i	0.987534	−	0.157403i	$-0.0503122\pi$
$499$	10.3694	+	15.5190i	0.464200	+	0.694724i	−0.523335	+	0.852127i	$0.675312\pi$
$500$	1.97826	−	0.294097i	0.0884704	−	0.0131524i
$501$	−17.9722	−	26.6642i	−0.802938	−	1.19127i
$502$	24.2672	+	10.7522i	1.08310	+	0.479896i
$503$	−16.9628	−	7.02623i	−0.756335	−	0.313284i	−0.0290116	−	0.999579i	$-0.509236\pi$
$503$	−16.9628	−	7.02623i	−0.756335	−	0.313284i	−0.727323	+	0.686295i	$0.759236\pi$
$504$	−17.1327	−	4.58420i	−0.763153	−	0.204196i
$505$	2.75189	−	1.13987i	0.122457	−	0.0507235i
$506$	−0.0636056	+	2.60810i	−0.00282762	+	0.115944i
$507$	2.99299	−	15.3700i	0.132924	−	0.682605i
$508$	−3.26273	−	9.10948i	−0.144760	−	0.404168i
$509$	−22.8805	−	4.55121i	−1.01416	−	0.201729i	−0.340087	−	0.940394i	$-0.610457\pi$
$509$	−22.8805	−	4.55121i	−1.01416	−	0.201729i	−0.674073	+	0.738665i	$0.735457\pi$
$510$	−9.87720	−	15.4542i	−0.437370	−	0.684326i
$511$		−	3.83107i		−	0.169477i
$512$	0.522567	−	22.6214i	0.0230944	−	0.999733i
$513$	−1.61453	+	4.03501i	−0.0712834	+	0.178150i
$514$	−6.31224	−	36.3436i	−0.278421	−	1.60305i
$515$	3.33140	−	16.7481i	0.146799	−	0.738010i
$516$	−6.97266	+	6.37509i	−0.306954	+	0.280648i
$517$	5.38197	+	3.59612i	0.236699	+	0.158157i
$518$	−9.85429	−	0.240324i	−0.432973	−	0.0105592i
$519$	−1.70876	+	1.72258i	−0.0750062	+	0.0756127i
$520$	−2.77645	−	4.89561i	−0.121755	−	0.214687i
$521$	−3.81031	+	9.19890i	−0.166933	+	0.403011i	−0.985103	−	0.171965i	$-0.944989\pi$
$521$	−3.81031	+	9.19890i	−0.166933	+	0.403011i	0.818170	+	0.574976i	$0.194989\pi$
$522$	−9.00287	−	22.7800i	−0.394045	−	0.997055i
$523$	−2.00342	−	10.0719i	−0.0876033	−	0.440412i	−0.999547	−	0.0300963i	$-0.990419\pi$
$523$	−2.00342	−	10.0719i	−0.0876033	−	0.440412i	0.911944	−	0.410315i	$-0.134581\pi$
$524$	1.71603	+	11.5430i	0.0749652	+	0.504257i
$525$	1.99916	−	3.01819i	0.0872503	−	0.131724i
$526$	−15.9063	+	10.0761i	−0.693548	+	0.439341i
$527$	−1.71028	+	1.71028i	−0.0745011	+	0.0745011i
$528$	2.93072	−	5.54513i	0.127543	−	0.241321i
$529$	13.3272	+	13.3272i	0.579443	+	0.579443i
$530$	4.57930	+	1.02754i	0.198912	+	0.0446336i
$531$	−6.62283	−	1.26201i	−0.287406	−	0.0547664i
$532$	−3.39186	−	0.848456i	−0.147056	−	0.0367853i
$533$	−18.7563	+	3.73086i	−0.812426	+	0.161602i
$534$	−1.08696	+	1.04358i	−0.0470372	+	0.0451601i
$535$	2.65351	+	1.09912i	0.114721	+	0.0475190i
$536$	0.618079	−	0.204517i	0.0266970	−	0.00883377i
$537$	23.4216	−	23.6110i	1.01072	−	1.01889i
$538$	5.02293	+	5.27405i	0.216554	+	0.227380i
$539$	−1.32341	+	1.98062i	−0.0570033	+	0.0853115i
$540$	−3.62213	−	9.74064i	−0.155872	−	0.419171i
$541$	−4.52837	−	0.900750i	−0.194690	−	0.0387262i	0.0967820	−	0.995306i	$-0.469145\pi$
$541$	−4.52837	−	0.900750i	−0.194690	−	0.0387262i	−0.291472	+	0.956579i	$0.594145\pi$
$542$	8.49147	+	5.97832i	0.364740	+	0.256791i
$543$	20.7058	−	8.67445i	0.888570	−	0.372256i
$544$	−3.14992	−	42.2395i	−0.135052	−	1.81100i
$545$	−18.2213			−0.780516
$546$	−9.94925	−	2.19046i	−0.425789	−	0.0937430i
$547$	−0.481046	+	2.41838i	−0.0205680	+	0.103402i	−0.989706	−	0.143118i	$-0.954287\pi$
$547$	−0.481046	+	2.41838i	−0.0205680	+	0.103402i	0.969138	+	0.246520i	$0.0792872\pi$
$548$	−1.79634	+	36.8068i	−0.0767356	+	1.57231i
$549$	8.66239	+	41.7872i	0.369702	+	1.78343i
$550$	0.882940	+	0.927083i	0.0376487	+	0.0395309i
$551$	−1.84792	−	4.46128i	−0.0787241	−	0.190057i
$552$	3.17419	+	9.46492i	0.135103	+	0.402854i
$553$	3.23601	−	7.81242i	0.137609	−	0.332218i
$554$	9.99653	+	25.9026i	0.424712	+	1.10050i
$555$	−3.22827	−	4.78958i	−0.137032	−	0.203306i
$556$	23.1882	+	38.6590i	0.983399	+	1.63951i
$557$	1.66136	−	1.11008i	0.0703939	−	0.0470357i	−0.519875	−	0.854242i	$-0.674022\pi$
$557$	1.66136	−	1.11008i	0.0703939	−	0.0470357i	0.590269	+	0.807206i	$0.299022\pi$
$558$	−1.15179	+	0.742687i	−0.0487591	+	0.0314404i
$559$	−3.83743	+	3.83743i	−0.162306	+	0.162306i
$560$	7.37082	−	3.94588i	0.311474	−	0.166744i
$561$	4.44923	−	10.8649i	0.187847	−	0.458718i
$562$	32.4821	−	20.5764i	1.37017	−	0.867962i
$563$	−3.41160	+	2.27956i	−0.143782	+	0.0960719i	−0.625381	−	0.780320i	$-0.715056\pi$
$563$	−3.41160	+	2.27956i	−0.143782	+	0.0960719i	0.481599	+	0.876392i	$0.340056\pi$
$564$	24.0523	+	5.91377i	1.01279	+	0.249015i
$565$	11.1811	−	2.22406i	0.470392	−	0.0935667i
$566$	29.9750	+	13.2813i	1.25994	+	0.558253i
$567$	−17.4930	−	6.91792i	−0.734638	−	0.290526i
$568$	2.98106	−	3.82368i	0.125082	−	0.160438i
$569$	15.4647	+	37.3351i	0.648315	+	1.56517i	0.815191	+	0.579192i	$0.196632\pi$
$569$	15.4647	+	37.3351i	0.648315	+	1.56517i	−0.166876	+	0.985978i	$0.553368\pi$
$570$	−0.745329	−	1.90836i	−0.0312184	−	0.0799322i
$571$	24.6313	−	36.8634i	1.03079	−	1.54268i	0.204954	−	0.978772i	$-0.434296\pi$
$571$	24.6313	−	36.8634i	1.03079	−	1.54268i	0.825835	−	0.563913i	$-0.190704\pi$
$572$	1.53932	−	3.25732i	0.0643620	−	0.136195i
$573$	−41.5313	+	8.43508i	−1.73500	+	0.352380i
$574$	−4.86125	−	27.9893i	−0.202904	−	1.16825i
$575$	−2.03777			−0.0849809
$576$	3.30730	−	23.7710i	0.137804	−	0.990459i
$577$	36.7016			1.52791			0.763955	−	0.645270i	$-0.223255\pi$
$577$	36.7016			1.52791			0.763955	+	0.645270i	$0.223255\pi$
$578$	−9.45387	−	54.4320i	−0.393229	−	2.26407i
$579$	−26.5600	+	5.39438i	−1.10380	+	0.224183i
$580$	10.4398	+	4.93355i	0.433489	+	0.204855i
$581$	−11.9115	+	17.8268i	−0.494173	+	0.739581i
$582$	−6.96049	−	17.8218i	−0.288522	−	0.738737i
$583$	1.14967	+	2.77556i	0.0476146	+	0.114952i
$584$	5.14500	−	0.637095i	0.212902	−	0.0263632i
$585$	−2.32877	−	5.49654i	−0.0962829	−	0.227254i
$586$	−11.5449	−	5.11530i	−0.476917	−	0.211311i
$587$	36.5667	−	7.27357i	1.50927	−	0.300212i	0.630022	−	0.776578i	$-0.283046\pi$
$587$	36.5667	−	7.27357i	1.50927	−	0.300212i	0.879247	+	0.476365i	$0.158046\pi$
$588$	−2.17633	+	8.85151i	−0.0897503	+	0.365030i
$589$	−0.224643	+	0.150102i	−0.00925625	+	0.00618483i
$590$	2.68485	−	1.70076i	0.110533	−	0.0700194i
$591$	−4.29004	+	10.4762i	−0.176469	+	0.430933i
$592$	−1.31599	−	13.2739i	−0.0540869	−	0.545556i
$593$	−3.78578	+	3.78578i	−0.155463	+	0.155463i	−0.780553	−	0.625090i	$-0.785062\pi$
$593$	−3.78578	+	3.78578i	−0.155463	+	0.155463i	0.625090	+	0.780553i	$0.285062\pi$
$594$	3.76366	−	5.48540i	0.154425	−	0.225069i
$595$	13.0128	−	8.69485i	0.533471	−	0.356454i
$596$	−8.49261	+	5.09399i	−0.347871	+	0.208658i
$597$	4.63191	+	6.87209i	0.189572	+	0.281256i
$598$	2.06464	+	5.34982i	0.0844295	+	0.218771i
$599$	−5.98340	+	14.4452i	−0.244475	+	0.590215i	−0.997717	−	0.0675279i	$-0.978489\pi$
$599$	−5.98340	+	14.4452i	−0.244475	+	0.590215i	0.753242	+	0.657743i	$0.228489\pi$
$600$	4.38577	+	2.18288i	0.179048	+	0.0891159i
$601$	12.8826	+	31.1013i	0.525492	+	1.26865i	0.934449	+	0.356096i	$0.115892\pi$
$601$	12.8826	+	31.1013i	0.525492	+	1.26865i	−0.408958	+	0.912553i	$0.634108\pi$
$602$	−5.55982	−	5.83778i	−0.226601	−	0.237930i
$603$	0.676154	−	0.140165i	0.0275351	−	0.00570796i
$604$	−14.9732	−	0.730761i	−0.609252	−	0.0297342i
$605$	1.98611	−	9.98485i	0.0807469	−	0.405942i
$606$	7.12546	+	1.56876i	0.289452	+	0.0637266i
$607$	−29.8395			−1.21115			−0.605575	−	0.795788i	$-0.707057\pi$
$607$	−29.8395			−1.21115			−0.605575	+	0.795788i	$0.707057\pi$
$608$	0.575394	−	4.69624i	0.0233353	−	0.190458i
$609$	19.2777	−	8.07619i	0.781173	−	0.327264i
$610$	−16.4496	−	11.5812i	−0.666025	−	0.468908i
$611$	13.9542	+	2.77566i	0.564525	+	0.112291i
$612$	1.82856	−	44.8889i	0.0739152	−	1.81453i
$613$	19.4691	−	29.1376i	0.786351	−	1.17686i	−0.194271	−	0.980948i	$-0.562234\pi$
$613$	19.4691	−	29.1376i	0.786351	−	1.17686i	0.980622	−	0.195910i	$-0.0627660\pi$
$614$	22.8080	+	23.9483i	0.920455	+	0.966473i
$615$	11.7232	−	11.8180i	0.472724	−	0.476546i
$616$	4.78156	+	2.40394i	0.192655	+	0.0968577i
$617$	−8.43270	−	3.49294i	−0.339488	−	0.140620i	0.206425	−	0.978462i	$-0.433817\pi$
$617$	−8.43270	−	3.49294i	−0.339488	−	0.140620i	−0.545913	+	0.837842i	$0.683817\pi$
$618$	30.1728	−	28.9687i	1.21373	−	1.16529i
$619$	−23.2650	+	4.62770i	−0.935100	+	0.186003i	−0.639046	−	0.769168i	$-0.720671\pi$
$619$	−23.2650	+	4.62770i	−0.935100	+	0.186003i	−0.296054	+	0.955171i	$0.595671\pi$
$620$	0.156775	−	0.626738i	0.00629625	−	0.0251704i
$621$	2.19102	+	10.3594i	0.0879226	+	0.415708i
$622$	22.0548	+	4.94884i	0.884315	+	0.198430i
$623$	−0.909178	−	0.909178i	−0.0364254	−	0.0364254i
$624$	1.28718	−	13.7258i	0.0515286	−	0.549471i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	14.6881	−	9.30448i	0.587056	−	0.371882i
$627$	0.724212	−	1.09336i	0.0289222	−	0.0436648i
$628$	12.8032	−	1.90338i	0.510902	−	0.0759531i
$629$	−4.87133	−	24.4898i	−0.194233	−	0.976473i
$630$	8.24702	−	3.25930i	0.328569	−	0.129853i
$631$	11.1245	−	26.8569i	0.442860	−	1.06916i	−0.532081	−	0.846693i	$-0.678590\pi$
$631$	11.1245	−	26.8569i	0.442860	−	1.06916i	0.974941	−	0.222464i	$-0.0714101\pi$
$632$	11.0300	+	3.04667i	0.438748	+	0.121190i
$633$	−4.19244	+	4.22634i	−0.166635	+	0.167982i
$634$	−24.4276	−	0.595733i	−0.970143	−	0.0236596i
$635$	4.02272	+	2.68789i	0.159637	+	0.106666i
$636$	7.75712	+	8.48424i	0.307590	+	0.336422i
$637$	−1.02147	+	5.13528i	−0.0404721	+	0.203467i
$638$	1.26483	+	7.28245i	0.0500752	+	0.288315i
$639$	3.60692	−	3.66548i	0.142687	−	0.145004i
$640$	6.52493	+	9.24258i	0.257921	+	0.365345i
$641$			20.8332i			0.822861i	0.911441	+	0.411430i	$0.134971\pi$
$641$			20.8332i			0.822861i	−0.911441	+	0.411430i	$0.865029\pi$
$642$	3.78871	+	5.92796i	0.149528	+	0.233958i
$643$	−24.1182	−	4.79741i	−0.951128	−	0.189191i	−0.304942	−	0.952371i	$-0.598637\pi$
$643$	−24.1182	−	4.79741i	−0.951128	−	0.189191i	−0.646186	+	0.763180i	$0.723637\pi$
$644$	−8.01958	+	2.87236i	−0.316016	+	0.113187i
$645$	0.902918	−	4.63677i	0.0355524	−	0.182573i
$646$	0.215932	−	8.85411i	0.00849571	−	0.348360i
$647$	−31.0233	+	12.8503i	−1.21965	+	0.505197i	−0.897299	−	0.441423i	$-0.854474\pi$
$647$	−31.0233	+	12.8503i	−1.21965	+	0.505197i	−0.322354	+	0.946619i	$0.604474\pi$
$648$	6.38151	−	24.6430i	0.250689	−	0.968068i
$649$	1.87960	+	0.778556i	0.0737808	+	0.0305610i
$650$	2.57282	+	1.13996i	0.100914	+	0.0447128i
$651$	−0.653606	−	0.969715i	−0.0256168	−	0.0380061i
$652$	−5.98583	−	40.2640i	−0.234423	−	1.57686i
$653$	−0.975623	−	1.46012i	−0.0381791	−	0.0571390i	0.811889	−	0.583812i	$-0.198439\pi$
$653$	−0.975623	−	1.46012i	−0.0381791	−	0.0571390i	−0.850068	+	0.526673i	$0.823439\pi$
$654$	−36.5985	−	25.5470i	−1.43112	−	0.998967i
$655$	−4.12591	−	4.12591i	−0.161213	−	0.161213i
$656$	36.7803	−	11.1830i	1.43603	−	0.436624i
$657$	5.49860	−	0.0442814i	0.214521	−	0.00172758i
$658$	−4.62739	+	20.6222i	−0.180395	+	0.803938i
$659$	27.6638	+	41.4019i	1.07763	+	1.61279i	0.741475	+	0.670981i	$0.234127\pi$
$659$	27.6638	+	41.4019i	1.07763	+	1.61279i	0.336155	+	0.941807i	$0.390873\pi$
$660$	0.473628	+	3.10001i	0.0184359	+	0.120668i
$661$	7.29890	+	36.6940i	0.283894	+	1.42723i	0.814770	+	0.579784i	$0.196863\pi$
$661$	7.29890	+	36.6940i	0.283894	+	1.42723i	−0.530876	+	0.847449i	$0.678137\pi$
$662$	−12.5160	−	32.4310i	−0.486449	−	1.26047i
$663$	−0.103909	−	25.8061i	−0.00403551	−	1.00223i
$664$	−25.9217	−	13.0322i	−1.00596	−	0.505748i
$665$	1.61511	−	0.669000i	0.0626313	−	0.0259427i
$666$	0.231027	−	14.1463i	0.00895212	−	0.548157i
$667$	−9.78215	−	6.53623i	−0.378767	−	0.253084i
$668$	24.9439	+	27.5035i	0.965108	+	1.06414i
$669$	39.5536	−	8.03340i	1.52923	−	0.310589i
$670$	−0.187393	+	0.266169i	−0.00723964	+	0.0102830i
$671$		−	12.8778i		−	0.497142i
$672$	20.3370	+	2.40865i	0.784516	+	0.0929158i
$673$			45.4384i			1.75152i	0.482745	+	0.875761i	$0.339640\pi$
$673$			45.4384i			1.75152i	−0.482745	+	0.875761i	$0.660360\pi$
$674$	−14.8870	−	10.4810i	−0.573425	−	0.403713i
$675$	4.35500	+	2.83443i	0.167624	+	0.109097i
$676$	−0.881389	+	18.0596i	−0.0338996	+	0.694600i
$677$	4.78928	+	3.20009i	0.184067	+	0.122990i	0.644190	−	0.764866i	$-0.277195\pi$
$677$	4.78928	+	3.20009i	0.184067	+	0.122990i	−0.460123	+	0.887855i	$0.652195\pi$
$678$	25.5760	+	11.2092i	0.982241	+	0.430486i
$679$	15.0832	−	6.24767i	0.578841	−	0.239764i
$680$	13.8409	+	16.0298i	0.530773	+	0.614714i
$681$	−29.0701	+	0.117052i	−1.11397	+	0.00448545i
$682$	0.385820	−	0.148898i	0.0147738	−	0.00570162i
$683$	−1.86318	−	9.36682i	−0.0712925	−	0.358411i	0.928628	−	0.371012i	$-0.120989\pi$
$683$	−1.86318	−	9.36682i	−0.0712925	−	0.358411i	−0.999921	+	0.0126003i	$0.995989\pi$
$684$	1.17855	−	4.87801i	0.0450631	−	0.186516i
$685$	−10.2365	−	15.3201i	−0.391118	−	0.585350i
$686$	−27.7785	−	6.23318i	−1.06059	−	0.237984i
$687$	−10.6035	+	25.8936i	−0.404551	+	0.987904i
$688$	6.91536	−	8.43746i	0.263646	−	0.321675i
$689$	4.66933	+	4.66933i	0.177887	+	0.177887i
$690$	−4.09297	−	2.85703i	−0.155817	−	0.108765i
$691$	11.9151	+	17.8322i	0.453271	+	0.678368i	0.985777	−	0.168058i	$-0.0537495\pi$
$691$	11.9151	+	17.8322i	0.453271	+	0.678368i	−0.532506	+	0.846426i	$0.678750\pi$
$692$	1.66824	−	2.25088i	0.0634171	−	0.0855656i
$693$	4.74507	+	3.11558i	0.180250	+	0.118351i
$694$	9.46364	−	21.3589i	0.359235	−	0.810773i
$695$	−20.8243	−	8.62569i	−0.789910	−	0.327191i
$696$	14.0519	+	24.5463i	0.532635	+	0.930425i
$697$	66.4842	−	27.5387i	2.51827	−	1.04310i
$698$	−34.4253	−	0.839554i	−1.30302	−	0.0317776i
$699$	−23.9770	−	4.66904i	−0.906893	−	0.176599i
$700$	−1.78609	+	3.77950i	−0.0675077	+	0.142852i
$701$	−28.4953	−	5.66807i	−1.07625	−	0.214080i	−0.375023	−	0.927016i	$-0.622365\pi$
$701$	−28.4953	−	5.66807i	−1.07625	−	0.214080i	−0.701229	+	0.712936i	$0.747365\pi$
$702$	3.02889	−	14.3051i	0.114318	−	0.539912i
$703$		−	2.78917i		−	0.105196i
$704$	−2.43326	+	6.82124i	−0.0917069	+	0.257085i
$705$	−11.4225	+	4.78531i	−0.430195	+	0.180225i
$706$	−12.8608	+	2.23369i	−0.484023	+	0.0840662i
$707$	−1.21458	+	6.10611i	−0.0456790	+	0.229644i
$708$	7.77720	+	0.348178i	0.292285	+	0.0130853i
$709$	−1.36725	−	0.913567i	−0.0513481	−	0.0343097i	0.529631	−	0.848228i	$-0.322330\pi$
$709$	−1.36725	−	0.913567i	−0.0513481	−	0.0343097i	−0.580979	+	0.813918i	$0.697330\pi$
$710$	−0.0591034	+	2.42349i	−0.00221811	+	0.0909520i
$711$	11.2503	+	4.55423i	0.421919	+	0.170797i
$712$	1.06980	−	1.37219i	0.0400925	−	0.0514249i
$713$	−0.251901	+	0.608143i	−0.00943377	+	0.0227751i
$714$	38.3274	+	0.780313i	1.43437	+	0.0292025i
$715$	0.351428	+	1.76675i	0.0131427	+	0.0660727i
$716$	−22.8662	+	30.8523i	−0.854552	+	1.15300i
$717$	12.8939	+	8.54052i	0.481531	+	0.318952i
$718$	−8.90550	−	14.0583i	−0.332350	−	0.524652i
$719$	36.4623	−	36.4623i	1.35981	−	1.35981i	0.485675	−	0.874139i	$-0.338574\pi$
$719$	36.4623	−	36.4623i	1.35981	−	1.35981i	0.874139	−	0.485675i	$-0.161426\pi$
$720$	5.74858	+	10.5335i	0.214237	+	0.392559i
$721$	25.2378	+	25.2378i	0.939906	+	0.939906i
$722$	−5.66644	+	25.2528i	−0.210883	+	0.939812i
$723$	2.28795	−	3.45418i	0.0850896	−	0.128462i
$724$	−22.2300	+	13.3339i	−0.826172	+	0.495550i
$725$	−5.66248	+	1.12634i	−0.210299	+	0.0418311i
$726$	17.9884	−	17.2705i	0.667610	−	0.640969i
$727$	26.1677	+	10.8390i	0.970506	+	0.401997i	0.810900	−	0.585184i	$-0.198978\pi$
$727$	26.1677	+	10.8390i	0.970506	+	0.401997i	0.159605	+	0.987181i	$0.448978\pi$
$728$	11.7321	+	0.859721i	0.434820	+	0.0318634i
$729$	9.72685	−	25.1871i	0.360254	−	0.932854i
$730$	−1.87707	+	1.78769i	−0.0694734	+	0.0661655i
$731$	11.3455	−	16.9797i	0.419629	−	0.628019i
$732$	−16.8027	−	46.3244i	−0.621045	−	1.71220i
$733$	−6.92754	−	1.37797i	−0.255875	−	0.0508966i	0.0654861	−	0.997853i	$-0.479140\pi$
$733$	−6.92754	−	1.37797i	−0.255875	−	0.0508966i	−0.321361	+	0.946957i	$0.604140\pi$
$734$	−14.2557	+	20.2484i	−0.526187	+	0.747383i
$735$	−1.76105	−	4.20359i	−0.0649571	−	0.155052i
$736$	−5.19111	−	10.2924i	−0.191347	−	0.379381i
$737$	−0.208374			−0.00767556
$738$	40.1159	−	7.30068i	1.47669	−	0.268742i
$739$	7.36375	−	37.0201i	0.270880	−	1.36181i	−0.570471	−	0.821317i	$-0.693240\pi$
$739$	7.36375	−	37.0201i	0.270880	−	1.36181i	0.841351	−	0.540488i	$-0.181760\pi$
$740$	4.48056	+	4.94034i	0.164709	+	0.181611i
$741$	0.550986	−	2.82949i	0.0202410	−	0.103944i
$742$	−7.10334	+	6.76512i	−0.260772	+	0.248355i
$743$	10.9409	+	26.4137i	0.401383	+	0.969025i	0.987331	+	0.158676i	$0.0507225\pi$
$743$	10.9409	+	26.4137i	0.401383	+	0.969025i	−0.585948	+	0.810349i	$0.699278\pi$
$744$	1.19360	−	1.03903i	0.0437596	−	0.0380927i
$745$	1.89489	−	4.57468i	0.0694235	−	0.167603i
$746$	−35.7651	+	13.8027i	−1.30945	+	0.505354i
$747$	−25.7239	−	16.8901i	−0.941187	−	0.617976i
$748$	−3.28983	+	13.1517i	−0.120288	+	0.480873i
$749$	−4.99145	+	3.33518i	−0.182384	+	0.121865i
$750$	−2.41165	+	0.428871i	−0.0880611	+	0.0156602i
$751$	8.61340	−	8.61340i	0.314307	−	0.314307i	−0.532268	−	0.846576i	$-0.678660\pi$
$751$	8.61340	−	8.61340i	0.314307	−	0.314307i	0.846576	+	0.532268i	$0.178660\pi$
$752$	−28.4645	−	2.78502i	−1.03799	−	0.101559i
$753$	−30.0832	−	12.3192i	−1.09629	−	0.448937i
$754$	8.69416	+	13.7247i	0.316623	+	0.499824i
$755$	6.23230	−	4.16429i	0.226817	−	0.151554i
$756$	21.1342	+	5.01617i	0.768645	+	0.182436i
$757$	−34.5516	+	6.87274i	−1.25580	+	0.249794i	−0.777770	−	0.628549i	$-0.783649\pi$
$757$	−34.5516	+	6.87274i	−1.25580	+	0.249794i	−0.478030	+	0.878343i	$0.658649\pi$
$758$	1.24761	−	2.81579i	0.0453153	−	0.102274i
$759$	−0.0128655	−	3.19518i	−0.000466990	−	0.115978i
$760$	1.16703	+	2.05779i	0.0423327	+	0.0746437i
$761$	2.94028	+	7.09847i	0.106585	+	0.257319i	0.968170	−	0.250295i	$-0.0805275\pi$
$761$	2.94028	+	7.09847i	0.106585	+	0.257319i	−0.861584	+	0.507614i	$0.830528\pi$
$762$	4.31132	+	11.0388i	0.156182	+	0.399893i
$763$	21.1590	−	31.6666i	0.766006	−	1.14641i
$764$	46.0695	−	16.5006i	1.66674	−	0.596972i
$765$	12.6298	+	18.5762i	0.456632	+	0.671626i
$766$	47.9006	−	8.31947i	1.73072	−	0.300595i
$767$	4.47183			0.161468
$768$	0.147236	+	27.7124i	0.00531292	+	0.999986i
$769$	−33.6382			−1.21302			−0.606512	−	0.795074i	$-0.707432\pi$
$769$	−33.6382			−1.21302			−0.606512	+	0.795074i	$0.707432\pi$
$770$	−2.63645	+	0.457905i	−0.0950112	+	0.0165017i
$771$	8.99214	+	44.2741i	0.323844	+	1.59449i
$772$	29.4623	−	10.5525i	1.06037	−	0.379791i
$773$	1.92464	−	2.88043i	0.0692244	−	0.103602i	−0.795242	−	0.606292i	$-0.792656\pi$
$773$	1.92464	−	2.88043i	0.0692244	−	0.103602i	0.864467	+	0.502690i	$0.167656\pi$
$774$	8.31449	−	8.04728i	0.298858	−	0.289254i
$775$	0.123616	+	0.298435i	0.00444042	+	0.0107201i
$776$	10.8987	+	19.2173i	0.391241	+	0.689860i
$777$	12.0725	−	0.0486104i	0.433098	−	0.00174389i
$778$	22.0393	−	49.7415i	0.790148	−	1.78332i
$779$	7.88389	−	1.56820i	0.282470	−	0.0561867i
$780$	3.56939	+	5.89686i	0.127805	+	0.211141i
$781$	−1.29028	+	0.862140i	−0.0461700	+	0.0308498i
$782$	−11.5473	−	18.2287i	−0.412930	−	0.651856i
$783$	11.8143	+	27.5753i	0.422208	+	0.985460i
$784$	1.02492	−	10.4752i	0.0366042	−	0.374115i
$785$	−4.57635	+	4.57635i	−0.163337	+	0.163337i
$786$	−2.50243	−	14.0718i	−0.0892586	−	0.501924i
$787$	−0.551478	+	0.368486i	−0.0196581	+	0.0131351i	−0.565360	−	0.824844i	$-0.691263\pi$
$787$	−0.551478	+	0.368486i	−0.0196581	+	0.0131351i	0.545702	+	0.837979i	$0.316263\pi$
$788$	3.17212	−	12.6811i	0.113002	−	0.451747i
$789$	19.1228	−	12.8891i	0.680788	−	0.458864i
$790$	−5.33779	+	2.06000i	−0.189910	+	0.0732914i
$791$	−9.11854	+	22.0141i	−0.324218	+	0.782731i
$792$	−3.39503	+	6.89059i	−0.120637	+	0.244846i
$793$	−10.8322	−	26.1512i	−0.384662	−	0.928657i
$794$	−22.2359	+	21.1772i	−0.789123	+	0.751550i
$795$	−5.64196	−	1.09866i	−0.200100	−	0.0389654i
$796$	−6.42870	−	7.08840i	−0.227859	−	0.251242i
$797$	−8.23595	+	41.4049i	−0.291732	+	1.46664i	0.505427	+	0.862869i	$0.331335\pi$
$797$	−8.23595	+	41.4049i	−0.291732	+	1.46664i	−0.797159	+	0.603769i	$0.793665\pi$
$798$	4.18200	+	0.920722i	0.148041	+	0.0325932i
$799$	−53.5377			−1.89403
$800$	−5.37277	−	1.77013i	−0.189956	−	0.0625836i
$801$	1.29440	−	1.31542i	0.0457354	−	0.0464780i
$802$	−0.875470	+	1.24350i	−0.0309139	+	0.0439094i
$803$	−1.62743	−	0.323716i	−0.0574307	−	0.0114237i
$804$	−0.749569	+	0.271882i	−0.0264353	+	0.00958855i
$805$	2.36630	−	3.54142i	0.0834011	−	0.124819i
$806$	0.658246	−	0.626904i	0.0231857	−	0.0220817i
$807$	−6.33280	−	6.28201i	−0.222925	−	0.221137i
$808$	−8.40229	−	0.615715i	−0.295591	−	0.0216608i
$809$	−26.6403	−	11.0348i	−0.936621	−	0.387961i	−0.138435	−	0.990372i	$-0.544207\pi$
$809$	−26.6403	−	11.0348i	−0.936621	−	0.387961i	−0.798187	+	0.602410i	$0.794207\pi$
$810$	4.77327	+	11.7990i	0.167716	+	0.414574i
$811$	15.0845	−	3.00049i	0.529688	−	0.105362i	0.0770011	−	0.997031i	$-0.475466\pi$
$811$	15.0845	−	3.00049i	0.529688	−	0.105362i	0.452687	+	0.891670i	$0.350466\pi$
$812$	−20.6969	+	12.4143i	−0.726317	+	0.435656i
$813$	−10.6037	−	7.02355i	−0.371887	−	0.246327i
$814$	−0.934751	+	4.16577i	−0.0327630	+	0.146010i
$815$	14.3919	+	14.3919i	0.504127	+	0.504127i
$816$	5.32578	+	51.6021i	0.186440	+	1.80644i
$817$	1.61300	−	1.61300i	0.0564316	−	0.0564316i
$818$	−19.5310	−	30.8318i	−0.682885	−	1.07801i
$819$	12.2566	+	2.33554i	0.428280	+	0.0816104i
$820$	−11.4452	+	15.4425i	−0.399684	+	0.539274i
$821$	−3.36249	−	16.9044i	−0.117352	−	0.589966i	−0.994050	−	0.108926i	$-0.965259\pi$
$821$	−3.36249	−	16.9044i	−0.117352	−	0.589966i	0.876698	−	0.481040i	$-0.159741\pi$
$822$	0.918672	−	45.1232i	0.0320424	−	1.57385i
$823$	−18.8908	+	45.6064i	−0.658491	+	1.58974i	0.141643	+	0.989918i	$0.454762\pi$
$823$	−18.8908	+	45.6064i	−0.658491	+	1.58974i	−0.800134	+	0.599821i	$0.795238\pi$
$824$	−29.6966	+	38.0905i	−1.03453	+	1.32695i
$825$	−1.11319	−	1.10426i	−0.0387564	−	0.0384456i
$826$	−0.161957	+	6.64092i	−0.00563521	+	0.231067i
$827$	6.99485	+	4.67381i	0.243235	+	0.162524i	0.671213	−	0.741265i	$-0.265774\pi$
$827$	6.99485	+	4.67381i	0.243235	+	0.162524i	−0.427978	+	0.903789i	$0.640774\pi$
$828$	−4.21529	−	11.4770i	−0.146491	−	0.398853i
$829$	1.96543	−	9.88090i	0.0682624	−	0.343178i	−0.931528	−	0.363670i	$-0.881523\pi$
$829$	1.96543	−	9.88090i	0.0682624	−	0.343178i	0.999790	+	0.0204925i	$0.00652342\pi$
$830$	14.2927	−	2.48238i	0.496106	−	0.0861648i
$831$	−13.1394	−	31.3635i	−0.455801	−	1.08799i
$832$	0.796434	+	15.8988i	0.0276114	+	0.551191i
$833$		−	19.7024i		−	0.682649i
$834$	−29.7331	−	46.5216i	−1.02957	−	1.61091i
$835$	−18.2083	−	3.62186i	−0.630125	−	0.125340i
$836$	−0.647025	+	1.36916i	−0.0223778	+	0.0473533i
$837$	1.38424	−	0.949305i	0.0478464	−	0.0328128i
$838$	−4.55002	−	0.110965i	−0.157178	−	0.00383321i
$839$	21.1701	−	8.76896i	0.730874	−	0.302738i	0.0139629	−	0.999903i	$-0.495555\pi$
$839$	21.1701	−	8.76896i	0.730874	−	0.302738i	0.716911	+	0.697165i	$0.245555\pi$
$840$	−8.88646	+	5.08718i	−0.306612	+	0.175524i
$841$	−4.00256	−	1.65791i	−0.138019	−	0.0571694i
$842$	−4.37193	+	9.86721i	−0.150667	+	0.340046i
$843$	−39.0504	+	26.3207i	−1.34497	+	0.906533i
$844$	4.09304	−	5.52254i	0.140888	−	0.190094i
$845$	−5.02266	−	7.51694i	−0.172785	−	0.258590i
$846$	−29.6518	−	6.40317i	−1.01945	−	0.220145i
$847$	15.0462	+	15.0462i	0.516995	+	0.516995i
$848$	−10.2666	−	8.41452i	−0.352556	−	0.288956i
$849$	−37.1590	−	15.2168i	−1.27529	−	0.522238i
$850$	−10.3323	−	2.31844i	−0.354394	−	0.0795219i
$851$	−3.77536	−	5.65022i	−0.129418	−	0.193687i
$852$	−3.51654	+	4.78485i	−0.120475	+	0.163926i
$853$	−2.13064	−	10.7115i	−0.0729518	−	0.366754i	0.927014	−	0.375027i	$-0.122367\pi$
$853$	−2.13064	−	10.7115i	−0.0729518	−	0.366754i	−0.999966	+	0.00827322i	$0.997367\pi$
$854$	39.2284	−	15.1393i	1.34237	−	0.518056i
$855$	0.978860	+	2.31038i	0.0334763	+	0.0790132i
$856$	−5.30910	−	6.14872i	−0.181461	−	0.210159i
$857$	−17.6378	+	7.30580i	−0.602495	+	0.249561i	−0.663016	−	0.748605i	$-0.730724\pi$
$857$	−17.6378	+	7.30580i	−0.602495	+	0.249561i	0.0605211	+	0.998167i	$0.480724\pi$
$858$	−1.77119	+	4.04133i	−0.0604673	+	0.137969i
$859$	−16.5416	−	11.0528i	−0.564394	−	0.377116i	0.240397	−	0.970675i	$-0.422722\pi$
$859$	−16.5416	−	11.0528i	−0.564394	−	0.377116i	−0.804791	+	0.593559i	$0.797722\pi$
$860$	−0.265895	+	5.44817i	−0.00906694	+	0.185781i
$861$	6.92512	+	34.0968i	0.236007	+	1.16202i
$862$	34.1409	+	24.0365i	1.16284	+	0.818687i
$863$			39.8099i			1.35515i	0.735455	+	0.677573i	$0.236968\pi$
$863$			39.8099i			1.35515i	−0.735455	+	0.677573i	$0.763032\pi$
$864$	−3.22199	+	29.2168i	−0.109614	+	0.993974i
$865$			1.40085i			0.0476302i
$866$	23.9256	−	33.9834i	0.813026	−	1.15480i
$867$	13.4676	+	66.3095i	0.457383	+	2.25199i
$868$	0.907149	+	1.00024i	0.0307907	+	0.0339503i
$869$	−3.04526	−	2.03478i	−0.103303	−	0.0690251i
$870$	−12.9526	−	5.67671i	−0.439133	−	0.192458i
$871$	−0.423149	+	0.175274i	−0.0143379	+	0.00593894i
$872$	46.0459	+	23.1497i	1.55931	+	0.783949i
$873$	9.14140	+	21.5762i	0.309389	+	0.730243i
$874$	−0.867837	−	2.24871i	−0.0293550	−	0.0760636i
$875$	−0.407766	−	2.04998i	−0.0137850	−	0.0693019i
$876$	−6.27660	+	0.958957i	−0.212067	+	0.0324001i
$877$	−29.5368	−	44.2049i	−0.997387	−	1.49269i	−0.865173	−	0.501473i	$-0.832792\pi$
$877$	−29.5368	−	44.2049i	−0.997387	−	1.49269i	−0.132214	−	0.991221i	$-0.542208\pi$
$878$	−5.89336	+	26.2641i	−0.198891	+	0.886370i
$879$	14.3119	+	5.86077i	0.482727	+	0.197679i
$880$	−1.05338	−	3.46452i	−0.0355096	−	0.116789i
$881$	−14.0452	−	14.0452i	−0.473196	−	0.473196i	0.429751	−	0.902947i	$-0.358601\pi$
$881$	−14.0452	−	14.0452i	−0.473196	−	0.473196i	−0.902947	+	0.429751i	$0.858601\pi$
$882$	2.35643	−	10.9122i	0.0793452	−	0.367432i
$883$	1.94299	+	2.90789i	0.0653868	+	0.0978582i	0.862722	−	0.505678i	$-0.168758\pi$
$883$	1.94299	+	2.90789i	0.0653868	+	0.0978582i	−0.797335	+	0.603537i	$0.793758\pi$
$884$	4.38184	+	29.4746i	0.147377	+	0.991340i
$885$	−3.22776	+	2.17557i	−0.108500	+	0.0731309i
$886$	9.63491	+	4.26901i	0.323691	+	0.143420i
$887$	−3.13191	−	1.29728i	−0.105159	−	0.0435584i	0.329483	−	0.944161i	$-0.393125\pi$
$887$	−3.13191	−	1.29728i	−0.105159	−	0.0435584i	−0.434643	+	0.900603i	$0.643125\pi$
$888$	2.07290	+	16.2049i	0.0695619	+	0.543799i
$889$	−9.34252	+	3.86980i	−0.313338	+	0.129789i
$890$	−0.0212102	+	0.869709i	−0.000710969	+	0.0291527i
$891$	−4.41683	+	6.84644i	−0.147969	+	0.229364i
$892$	−43.8757	+	15.7149i	−1.46907	+	0.526173i
$893$	−5.86539	−	1.16670i	−0.196278	−	0.0390421i
$894$	10.2199	−	6.53177i	0.341804	−	0.218455i
$895$		−	19.2011i		−	0.641822i
$896$	−23.6395	+	0.606942i	−0.789739	+	0.0202765i
$897$	−2.71376	−	6.47770i	−0.0906098	−	0.216284i
$898$	0.256442	+	1.47650i	0.00855757	+	0.0492715i
$899$	−0.363834	+	1.82912i	−0.0121346	+	0.0610045i
$900$	−5.44523	−	2.51982i	−0.181508	−	0.0839939i
$901$	−20.6607	−	13.8051i	−0.688309	−	0.459913i
$902$	−12.3006	−	0.299982i	−0.409564	−	0.00998832i
$903$	7.00971	+	6.95348i	0.233268	+	0.231397i
$904$	−31.0806	−	8.58501i	−1.03372	−	0.285533i
$905$	4.96002	−	11.9745i	0.164877	−	0.398047i
$906$	18.3564	+	0.373721i	0.609851	+	0.0124161i
$907$	11.0332	+	55.4678i	0.366352	+	1.84178i	0.520672	+	0.853757i	$0.325681\pi$
$907$	11.0332	+	55.4678i	0.366352	+	1.84178i	−0.154320	+	0.988021i	$0.549319\pi$
$908$	33.2027	−	4.93606i	1.10187	−	0.163809i
$909$	−8.77792	−	1.67267i	−0.291145	−	0.0554789i
$910$	−4.96873	+	3.14753i	−0.164712	+	0.104340i
$911$	−14.3281	+	14.3281i	−0.474711	+	0.474711i	−0.903435	−	0.428725i	$-0.858963\pi$
$911$	−14.3281	+	14.3281i	−0.474711	+	0.474711i	0.428725	+	0.903435i	$0.358963\pi$
$912$	−0.541045	+	5.76940i	−0.0179158	+	0.191044i
$913$	6.56629	+	6.56629i	0.217313	+	0.217313i
$914$	−2.39008	−	0.536306i	−0.0790567	−	0.0177394i
$915$	20.5413	+	13.6060i	0.679076	+	0.449800i
$916$	7.84043	−	31.3435i	0.259055	−	1.03562i
$917$	11.9614	−	2.37928i	0.395002	−	0.0785708i
$918$	−0.676949	+	55.0189i	−0.0223426	+	1.81589i
$919$	34.5897	+	14.3275i	1.14101	+	0.472621i	0.871509	−	0.490379i	$-0.163142\pi$
$919$	34.5897	+	14.3275i	1.14101	+	0.472621i	0.269499	+	0.963001i	$0.413142\pi$
$920$	5.14951	+	2.58893i	0.169774	+	0.0853546i
$921$	−28.7558	−	28.5252i	−0.947537	−	0.939937i
$922$	10.2365	+	10.7483i	0.337121	+	0.353975i
$923$	−1.89501	+	2.83609i	−0.0623751	+	0.0933510i
$924$	−5.93746	−	2.77668i	−0.195328	−	0.0913461i
$925$	−3.27068	−	0.650579i	−0.107539	−	0.0213909i
$926$	43.9121	+	30.9158i	1.44304	+	1.01596i
$927$	−35.9312	+	36.5147i	−1.18014	+	1.19930i
$928$	−20.1138	−	25.7307i	−0.660267	−	0.844653i
$929$	−39.7830			−1.30524			−0.652618	−	0.757687i	$-0.726330\pi$
$929$	−39.7830			−1.30524			−0.652618	+	0.757687i	$0.726330\pi$
$930$	−0.170128	+	0.772738i	−0.00557873	+	0.0253391i
$931$	0.429358	−	2.15853i	0.0140716	−	0.0707429i
$932$	28.1728	+	1.37496i	0.922830	+	0.0450382i
$933$	−27.1727	−	5.29134i	−0.889595	−	0.173231i
$934$	10.0406	+	10.5426i	0.328539	+	0.344964i
$935$	−2.59400	−	6.26248i	−0.0848330	−	0.204805i
$936$	−1.09832	+	16.8486i	−0.0358997	+	0.550713i
$937$	−6.46807	+	15.6153i	−0.211303	+	0.510130i	−0.993624	−	0.112745i	$-0.964036\pi$
$937$	−6.46807	+	15.6153i	−0.211303	+	0.510130i	0.782321	+	0.622875i	$0.214036\pi$
$938$	−0.244967	−	0.634750i	−0.00799846	−	0.0207253i
$939$	−17.6583	+	11.9020i	−0.576256	+	0.388407i
$940$	12.2633	−	7.35572i	0.399986	−	0.239917i
$941$	−31.6266	+	21.1322i	−1.03100	+	0.688891i	−0.951407	−	0.307937i	$-0.900361\pi$
$941$	−31.6266	+	21.1322i	−1.03100	+	0.688891i	−0.0795911	+	0.996828i	$0.525361\pi$
$942$	−15.6081	+	2.77563i	−0.508538	+	0.0904349i
$943$	13.8483	−	13.8483i	0.450962	−	0.450962i
$944$	−8.94547	+	0.886862i	−0.291150	+	0.0288649i
$945$	−9.98303	+	4.27711i	−0.324748	+	0.139134i
$946$	−2.94966	+	1.86852i	−0.0959018	+	0.0607508i
$947$	−10.3999	+	6.94901i	−0.337953	+	0.225813i	−0.712953	−	0.701212i	$-0.752643\pi$
$947$	−10.3999	+	6.94901i	−0.337953	+	0.225813i	0.375000	+	0.927025i	$0.377643\pi$
$948$	−13.6094	−	3.34616i	−0.442014	−	0.108678i
$949$	−3.57714	+	0.711538i	−0.116119	+	0.0230975i
$950$	−1.08144	−	0.479162i	−0.0350866	−	0.0155461i
$951$	29.9262	−	0.120499i	0.970424	−	0.00390746i
$952$	−43.9303	+	5.43980i	−1.42379	+	0.176305i
$953$	20.6431	+	49.8368i	0.668694	+	1.61437i	0.783797	+	0.621017i	$0.213280\pi$
$953$	20.6431	+	49.8368i	0.668694	+	1.61437i	−0.115102	+	0.993354i	$0.536720\pi$
$954$	−9.79183	−	10.1170i	−0.317022	−	0.327549i
$955$	−13.5935	+	20.3441i	−0.439876	+	0.658321i
$956$	−16.1463	−	7.63027i	−0.522208	−	0.246781i
$957$	−1.80182	−	8.87154i	−0.0582447	−	0.286776i
$958$	−7.29297	−	41.9903i	−0.235625	−	1.35665i
$959$	38.5115			1.24360
$960$	−8.30970	−	11.0882i	−0.268194	−	0.357871i
$961$	−30.8957			−0.996634
$962$	1.60583	+	9.24578i	0.0517739	+	0.298096i
$963$	−4.84456	−	7.12550i	−0.156114	−	0.229616i
$964$	−2.04410	+	4.32548i	−0.0658359	+	0.139314i
$965$	−8.69329	+	13.0104i	−0.279847	+	0.418821i
$966$	9.71804	−	3.79549i	0.312673	−	0.122118i
$967$	8.45704	+	20.4171i	0.271960	+	0.656570i	0.999567	−	0.0294246i	$-0.00936749\pi$
$967$	8.45704	+	20.4171i	0.271960	+	0.656570i	−0.727607	+	0.685994i	$0.759367\pi$
$968$	−17.7045	+	22.7087i	−0.569043	+	0.729887i
$969$	0.0436766	+	10.8472i	0.00140309	+	0.348461i
$970$	−10.0994	−	4.47481i	−0.324272	−	0.143677i
$971$	17.4293	−	3.46691i	0.559334	−	0.111259i	0.0926762	−	0.995696i	$-0.470458\pi$
$971$	17.4293	−	3.46691i	0.559334	−	0.111259i	0.466658	+	0.884438i	$0.345458\pi$
$972$	−6.95524	+	30.3912i	−0.223090	+	0.974798i
$973$	39.1720	−	26.1739i	1.25580	−	0.839098i
$974$	−28.9609	+	18.3458i	−0.927967	+	0.587838i
$975$	−3.18944	−	1.30609i	−0.102144	−	0.0418283i
$976$	26.8551	+	50.1648i	0.859612	+	1.60574i
$977$	−25.3045	+	25.3045i	−0.809562	+	0.809562i	−0.984567	−	0.175006i	$-0.944006\pi$
$977$	−25.3045	+	25.3045i	−0.809562	+	0.809562i	0.175006	+	0.984567i	$0.444006\pi$
$978$	8.72892	+	49.0849i	0.279120	+	1.56956i
$979$	−0.463039	+	0.309393i	−0.0147988	+	0.00988824i
$980$	2.70698	+	4.51303i	0.0864713	+	0.144164i
$981$	45.6945	+	30.0027i	1.45891	+	0.957912i
$982$	7.48343	+	19.3908i	0.238806	+	0.618785i
$983$	13.0485	−	31.5019i	0.416182	−	1.00475i	−0.567261	−	0.823538i	$-0.691997\pi$
$983$	13.0485	−	31.5019i	0.416182	−	1.00475i	0.983443	−	0.181215i	$-0.0580030\pi$
$984$	−44.6393	+	14.9704i	−1.42305	+	0.477239i
$985$	2.50119	+	6.03841i	0.0796946	+	0.192400i
$986$	−42.1627	−	44.2706i	−1.34273	−	1.40986i
$987$	4.94765	−	25.4078i	0.157485	−	0.808738i
$988$	−0.162256	+	3.32462i	−0.00516207	+	0.105770i
$989$	1.08425	−	5.45088i	0.0344770	−	0.173328i
$990$	−0.687688	−	3.77871i	−0.0218561	−	0.120095i
$991$	−30.2831			−0.961975			−0.480987	−	0.876728i	$-0.659722\pi$
$991$	−30.2831			−0.961975			−0.480987	+	0.876728i	$0.659722\pi$
$992$	−1.19243	+	1.38461i	−0.0378597	+	0.0439613i
$993$	16.4510	+	39.2683i	0.522057	+	1.24614i
$994$	−4.14312	−	2.91692i	−0.131412	−	0.0925191i
$995$	4.69277	+	0.933450i	0.148771	+	0.0295923i
$996$	32.1880	+	15.0529i	1.01992	+	0.476969i
$997$	6.26260	−	9.37264i	0.198338	−	0.296834i	−0.718947	−	0.695065i	$-0.755376\pi$
$997$	6.26260	−	9.37264i	0.198338	−	0.296834i	0.917285	+	0.398231i	$0.130376\pi$
$998$	18.2039	+	19.1140i	0.576234	+	0.605043i
$999$	0.209308	+	17.3266i	0.00662223	+	0.548190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.131.123	yes	1024
3.2	odd	2	inner	960.2.cn.a.131.6	✓	1024
64.43	odd	16	inner	960.2.cn.a.491.6	yes	1024
192.107	even	16	inner	960.2.cn.a.491.123	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.131.6	✓	1024	3.2	odd	2	inner
960.2.cn.a.131.123	yes	1024	1.1	even	1	trivial
960.2.cn.a.491.6	yes	1024	64.43	odd	16	inner
960.2.cn.a.491.123	yes	1024	192.107	even	16	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39335 - 0.242001i) q^{2} +(-1.69740 + 0.344744i) q^{3} +(1.88287 - 0.674385i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(-2.28164 + 0.891121i) q^{6} +(-0.799862 - 1.93104i) q^{7} +(2.46030 - 1.39531i) q^{8} +(2.76230 - 1.17033i) q^{9} +O(q^{10})\)	\(q+(1.39335 - 0.242001i) q^{2} +(-1.69740 + 0.344744i) q^{3} +(1.88287 - 0.674385i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(-2.28164 + 0.891121i) q^{6} +(-0.799862 - 1.93104i) q^{7} +(2.46030 - 1.39531i) q^{8} +(2.76230 - 1.17033i) q^{9} +(-0.572890 + 1.29298i) q^{10} +(-0.887886 + 0.176611i) q^{11} +(-2.96349 + 1.79381i) q^{12} +(-1.65449 + 1.10549i) q^{13} +(-1.58180 - 2.49705i) q^{14} +(0.656379 - 1.60286i) q^{15} +(3.09041 - 2.53956i) q^{16} +(5.29459 - 5.29459i) q^{17} +(3.56565 - 2.29917i) q^{18} +(0.695437 - 0.464676i) q^{19} +(-0.485336 + 1.94022i) q^{20} +(2.02340 + 3.00199i) q^{21} +(-1.19440 + 0.460951i) q^{22} +(0.779821 - 1.88265i) q^{23} +(-3.69508 + 3.21657i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(-2.03776 + 1.94073i) q^{26} +(-4.28526 + 2.93880i) q^{27} +(-2.80830 - 3.09648i) q^{28} +(1.12634 - 5.66248i) q^{29} +(0.526674 - 2.39220i) q^{30} -0.323024 q^{31} +(3.69146 - 4.28639i) q^{32} +(1.44621 - 0.605873i) q^{33} +(6.09595 - 8.65854i) q^{34} +(2.04998 + 0.407766i) q^{35} +(4.41181 - 4.06644i) q^{36} +(1.85269 - 2.77275i) q^{37} +(0.856538 - 0.815754i) q^{38} +(2.42721 - 2.44684i) q^{39} +(-0.206711 + 2.82086i) q^{40} +(8.87914 + 3.67786i) q^{41} +(3.54579 + 3.69317i) q^{42} +(2.67492 - 0.532075i) q^{43} +(-1.55267 + 0.931314i) q^{44} +(-0.561557 + 2.94697i) q^{45} +(0.630963 - 2.81192i) q^{46} +(-5.05588 - 5.05588i) q^{47} +(-4.37015 + 5.37604i) q^{48} +(1.86062 - 1.86062i) q^{49} +(-0.756793 - 1.19468i) q^{50} +(-7.16174 + 10.8123i) q^{51} +(-2.36966 + 3.19727i) q^{52} +(-0.647422 - 3.25481i) q^{53} +(-5.25969 + 5.13183i) q^{54} +(0.346436 - 0.836370i) q^{55} +(-4.66231 - 3.63488i) q^{56} +(-1.02024 + 1.02849i) q^{57} +(0.199063 - 8.16242i) q^{58} +(-1.86859 - 1.24855i) q^{59} +(0.154930 - 3.46064i) q^{60} +(-2.77520 + 13.9519i) q^{61} +(-0.450087 + 0.0781721i) q^{62} +(-4.46942 - 4.39801i) q^{63} +(4.10620 - 6.86579i) q^{64} -1.98984i q^{65} +(1.86846 - 1.19418i) q^{66} +(0.225754 + 0.0449052i) q^{67} +(6.39844 - 13.5396i) q^{68} +(-0.674631 + 3.46445i) q^{69} +(2.95503 + 0.0720664i) q^{70} +(1.58369 - 0.655987i) q^{71} +(5.16313 - 6.73366i) q^{72} +(1.69340 + 0.701430i) q^{73} +(1.91045 - 4.31177i) q^{74} +(0.968067 + 1.43626i) q^{75} +(0.996047 - 1.34392i) q^{76} +(1.05123 + 1.57328i) q^{77} +(2.78983 - 3.99670i) q^{78} +(2.86075 + 2.86075i) q^{79} +(0.394629 + 3.98049i) q^{80} +(6.26064 - 6.46563i) q^{81} +(13.2618 + 2.97580i) q^{82} +(-5.69890 - 8.52901i) q^{83} +(5.83429 + 4.28781i) q^{84} +(1.46078 + 7.34381i) q^{85} +(3.59835 - 1.38870i) q^{86} +(0.0402645 + 9.99977i) q^{87} +(-1.93804 + 1.67340i) q^{88} +(0.568334 - 0.235412i) q^{89} +(-0.0692786 + 4.24208i) q^{90} +(3.45812 + 2.31064i) q^{91} +(0.198668 - 4.07070i) q^{92} +(0.548300 - 0.111361i) q^{93} +(-8.26816 - 5.82111i) q^{94} +0.836395i q^{95} +(-4.78816 + 8.54831i) q^{96} +7.81094i q^{97} +(2.14223 - 3.04277i) q^{98} +(-2.24592 + 1.52698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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