LMFDB - Embedded newform 1110.2.l.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.262217 - 2.22064i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 + 2.69527i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.262217 - 2.22064i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 + 2.69527i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.22064 + 0.262217i) q^{10} -3.85429i q^{11} +(-0.707107 + 0.707107i) q^{12} +1.07171i q^{13} +(-2.69527 - 2.69527i) q^{14} +(-1.38481 - 1.75564i) q^{15} +1.00000 q^{16} -3.12620 q^{17} +1.00000 q^{18} +(-4.87828 + 4.87828i) q^{19} +(-0.262217 + 2.22064i) q^{20} +3.81169i q^{21} +3.85429 q^{22} -6.72404i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.86248 - 1.16458i) q^{25} -1.07171 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.69527 - 2.69527i) q^{28} +(0.240261 + 0.240261i) q^{29} +(1.75564 - 1.38481i) q^{30} +(-7.29610 + 7.29610i) q^{31} +1.00000i q^{32} +(-2.72539 - 2.72539i) q^{33} -3.12620i q^{34} +(5.27849 + 6.69198i) q^{35} +1.00000i q^{36} +(0.778980 - 6.03268i) q^{37} +(-4.87828 - 4.87828i) q^{38} +(0.757816 + 0.757816i) q^{39} +(-2.22064 - 0.262217i) q^{40} +9.24361i q^{41} -3.81169 q^{42} -8.98058i q^{43} +3.85429i q^{44} +(-2.22064 - 0.262217i) q^{45} +6.72404 q^{46} +(-3.13731 + 3.13731i) q^{47} +(0.707107 - 0.707107i) q^{48} -7.52901i q^{49} +(1.16458 - 4.86248i) q^{50} +(-2.21056 + 2.21056i) q^{51} -1.07171i q^{52} +(-6.75117 - 6.75117i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-8.55899 - 1.01066i) q^{55} +(2.69527 + 2.69527i) q^{56} +6.89894i q^{57} +(-0.240261 + 0.240261i) q^{58} +(-1.03632 + 1.03632i) q^{59} +(1.38481 + 1.75564i) q^{60} +(9.33589 - 9.33589i) q^{61} +(-7.29610 - 7.29610i) q^{62} +(2.69527 + 2.69527i) q^{63} -1.00000 q^{64} +(2.37989 + 0.281021i) q^{65} +(2.72539 - 2.72539i) q^{66} +(-0.0813396 - 0.0813396i) q^{67} +3.12620 q^{68} +(-4.75461 - 4.75461i) q^{69} +(-6.69198 + 5.27849i) q^{70} -9.73699 q^{71} -1.00000 q^{72} +(-3.77094 + 3.77094i) q^{73} +(6.03268 + 0.778980i) q^{74} +(-4.26178 + 2.61482i) q^{75} +(4.87828 - 4.87828i) q^{76} +(10.3884 + 10.3884i) q^{77} +(-0.757816 + 0.757816i) q^{78} +(-4.33967 + 4.33967i) q^{79} +(0.262217 - 2.22064i) q^{80} -1.00000 q^{81} -9.24361 q^{82} +(-5.06491 - 5.06491i) q^{83} -3.81169i q^{84} +(-0.819742 + 6.94217i) q^{85} +8.98058 q^{86} +0.339781 q^{87} -3.85429 q^{88} +(-4.92656 - 4.92656i) q^{89} +(0.262217 - 2.22064i) q^{90} +(-2.88856 - 2.88856i) q^{91} +6.72404i q^{92} +10.3182i q^{93} +(-3.13731 - 3.13731i) q^{94} +(9.55375 + 12.1121i) q^{95} +(0.707107 + 0.707107i) q^{96} -2.13394 q^{97} +7.52901 q^{98} -3.85429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	0.262217	−	2.22064i	0.117267	−	0.993100i
$5$	0.262217	−	2.22064i	0.117267	−	0.993100i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−2.69527	+	2.69527i	−1.01872	+	1.01872i	−0.0188964	+	0.999821i	$0.506015\pi$
$7$	−2.69527	+	2.69527i	−1.01872	+	1.01872i	−0.999821	+	0.0188964i	$0.993985\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	2.22064	+	0.262217i	0.702228	+	0.0829202i
$11$		−	3.85429i		−	1.16211i	−0.813864	−	0.581056i	$-0.802640\pi$
$11$		−	3.85429i		−	1.16211i	0.813864	−	0.581056i	$-0.197360\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$			1.07171i			0.297240i	0.988894	+	0.148620i	$0.0474831\pi$
$13$			1.07171i			0.297240i	−0.988894	+	0.148620i	$0.952517\pi$
$14$	−2.69527	−	2.69527i	−0.720342	−	0.720342i
$15$	−1.38481	−	1.75564i	−0.357558	−	0.453306i
$16$	1.00000			0.250000
$17$	−3.12620			−0.758216			−0.379108	−	0.925353i	$-0.623769\pi$
$17$	−3.12620			−0.758216			−0.379108	+	0.925353i	$0.623769\pi$
$18$	1.00000			0.235702
$19$	−4.87828	+	4.87828i	−1.11916	+	1.11916i	−0.127289	+	0.991866i	$0.540628\pi$
$19$	−4.87828	+	4.87828i	−1.11916	+	1.11916i	−0.991866	+	0.127289i	$0.959372\pi$
$20$	−0.262217	+	2.22064i	−0.0586334	+	0.496550i
$21$			3.81169i			0.831780i
$22$	3.85429			0.821737
$23$		−	6.72404i		−	1.40206i	−0.713133	−	0.701029i	$-0.752724\pi$
$23$		−	6.72404i		−	1.40206i	0.713133	−	0.701029i	$-0.247276\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−4.86248	−	1.16458i	−0.972497	−	0.232916i
$26$	−1.07171			−0.210180
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.69527	−	2.69527i	0.509359	−	0.509359i
$29$	0.240261	+	0.240261i	0.0446154	+	0.0446154i	0.729063	−	0.684447i	$-0.239956\pi$
$29$	0.240261	+	0.240261i	0.0446154	+	0.0446154i	−0.684447	+	0.729063i	$0.739956\pi$
$30$	1.75564	−	1.38481i	0.320535	−	0.252831i
$31$	−7.29610	+	7.29610i	−1.31042	+	1.31042i	−0.389312	+	0.921106i	$0.627287\pi$
$31$	−7.29610	+	7.29610i	−1.31042	+	1.31042i	−0.921106	+	0.389312i	$0.872713\pi$
$32$			1.00000i			0.176777i
$33$	−2.72539	−	2.72539i	−0.474430	−	0.474430i
$34$		−	3.12620i		−	0.536139i
$35$	5.27849	+	6.69198i	0.892227	+	1.13115i
$36$			1.00000i			0.166667i
$37$	0.778980	−	6.03268i	0.128063	−	0.991766i
$37$	0.778980	−	6.03268i	0.128063	−	0.991766i
$38$	−4.87828	−	4.87828i	−0.791362	−	0.791362i
$39$	0.757816	+	0.757816i	0.121348	+	0.121348i
$40$	−2.22064	−	0.262217i	−0.351114	−	0.0414601i
$41$			9.24361i			1.44361i	0.692097	+	0.721805i	$0.256687\pi$
$41$			9.24361i			1.44361i	−0.692097	+	0.721805i	$0.743313\pi$
$42$	−3.81169			−0.588157
$43$		−	8.98058i		−	1.36952i	−0.728766	−	0.684762i	$-0.759906\pi$
$43$		−	8.98058i		−	1.36952i	0.728766	−	0.684762i	$-0.240094\pi$
$44$			3.85429i			0.581056i
$45$	−2.22064	−	0.262217i	−0.331033	−	0.0390890i
$46$	6.72404			0.991405
$47$	−3.13731	+	3.13731i	−0.457623	+	0.457623i	−0.897874	−	0.440252i	$-0.854889\pi$
$47$	−3.13731	+	3.13731i	−0.457623	+	0.457623i	0.440252	+	0.897874i	$0.354889\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	7.52901i		−	1.07557i
$50$	1.16458	−	4.86248i	0.164696	−	0.687659i
$51$	−2.21056	+	2.21056i	−0.309540	+	0.309540i
$52$		−	1.07171i		−	0.148620i
$53$	−6.75117	−	6.75117i	−0.927345	−	0.927345i	0.0701888	−	0.997534i	$-0.477640\pi$
$53$	−6.75117	−	6.75117i	−0.927345	−	0.927345i	−0.997534	+	0.0701888i	$0.977640\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−8.55899	−	1.01066i	−1.15409	−	0.136277i
$56$	2.69527	+	2.69527i	0.360171	+	0.360171i
$57$			6.89894i			0.913786i
$58$	−0.240261	+	0.240261i	−0.0315478	+	0.0315478i
$59$	−1.03632	+	1.03632i	−0.134918	+	0.134918i	−0.771341	−	0.636423i	$-0.780413\pi$
$59$	−1.03632	+	1.03632i	−0.134918	+	0.134918i	0.636423	+	0.771341i	$0.280413\pi$
$60$	1.38481	+	1.75564i	0.178779	+	0.226653i
$61$	9.33589	−	9.33589i	1.19534	−	1.19534i	0.219791	−	0.975547i	$-0.429463\pi$
$61$	9.33589	−	9.33589i	1.19534	−	1.19534i	0.975547	−	0.219791i	$-0.0705375\pi$
$62$	−7.29610	−	7.29610i	−0.926605	−	0.926605i
$63$	2.69527	+	2.69527i	0.339573	+	0.339573i
$64$	−1.00000			−0.125000
$65$	2.37989	+	0.281021i	0.295189	+	0.0348564i
$66$	2.72539	−	2.72539i	0.335473	−	0.335473i
$67$	−0.0813396	−	0.0813396i	−0.00993722	−	0.00993722i	0.702121	−	0.712058i	$-0.252237\pi$
$67$	−0.0813396	−	0.0813396i	−0.00993722	−	0.00993722i	−0.712058	+	0.702121i	$0.752237\pi$
$68$	3.12620			0.379108
$69$	−4.75461	−	4.75461i	−0.572388	−	0.572388i
$70$	−6.69198	+	5.27849i	−0.799845	+	0.630900i
$71$	−9.73699			−1.15557			−0.577784	−	0.816190i	$-0.696082\pi$
$71$	−9.73699			−1.15557			−0.577784	+	0.816190i	$0.696082\pi$
$72$	−1.00000			−0.117851
$73$	−3.77094	+	3.77094i	−0.441355	+	0.441355i	−0.892467	−	0.451112i	$-0.851027\pi$
$73$	−3.77094	+	3.77094i	−0.441355	+	0.441355i	0.451112	+	0.892467i	$0.351027\pi$
$74$	6.03268	+	0.778980i	0.701284	+	0.0905546i
$75$	−4.26178	+	2.61482i	−0.492108	+	0.301933i
$76$	4.87828	−	4.87828i	0.559578	−	0.559578i
$77$	10.3884	+	10.3884i	1.18386	+	1.18386i
$78$	−0.757816	+	0.757816i	−0.0858058	+	0.0858058i
$79$	−4.33967	+	4.33967i	−0.488251	+	0.488251i	−0.907754	−	0.419503i	$-0.862204\pi$
$79$	−4.33967	+	4.33967i	−0.488251	+	0.488251i	0.419503	+	0.907754i	$0.362204\pi$
$80$	0.262217	−	2.22064i	0.0293167	−	0.248275i
$81$	−1.00000			−0.111111
$82$	−9.24361			−1.02079
$83$	−5.06491	−	5.06491i	−0.555946	−	0.555946i	0.372205	−	0.928151i	$-0.378602\pi$
$83$	−5.06491	−	5.06491i	−0.555946	−	0.555946i	−0.928151	+	0.372205i	$0.878602\pi$
$84$		−	3.81169i		−	0.415890i
$85$	−0.819742	+	6.94217i	−0.0889136	+	0.752984i
$86$	8.98058			0.968400
$87$	0.339781			0.0364283
$88$	−3.85429			−0.410869
$89$	−4.92656	−	4.92656i	−0.522215	−	0.522215i	0.396025	−	0.918240i	$-0.370389\pi$
$89$	−4.92656	−	4.92656i	−0.522215	−	0.522215i	−0.918240	+	0.396025i	$0.870389\pi$
$90$	0.262217	−	2.22064i	0.0276401	−	0.234076i
$91$	−2.88856	−	2.88856i	−0.302804	−	0.302804i
$92$			6.72404i			0.701029i
$93$			10.3182i			1.06995i
$94$	−3.13731	−	3.13731i	−0.323588	−	0.323588i
$95$	9.55375	+	12.1121i	0.980194	+	1.24267i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−2.13394			−0.216668			−0.108334	−	0.994115i	$-0.534552\pi$
$97$	−2.13394			−0.216668			−0.108334	+	0.994115i	$0.534552\pi$
$98$	7.52901			0.760544
$99$	−3.85429			−0.387371
$100$	4.86248	+	1.16458i	0.486248	+	0.116458i
$101$			15.9490i			1.58699i	0.608578	+	0.793494i	$0.291740\pi$
$101$			15.9490i			1.58699i	−0.608578	+	0.793494i	$0.708260\pi$
$102$	−2.21056	−	2.21056i	−0.218878	−	0.218878i
$103$	−7.78216			−0.766799			−0.383399	−	0.923583i	$-0.625247\pi$
$103$	−7.78216			−0.766799			−0.383399	+	0.923583i	$0.625247\pi$
$104$	1.07171			0.105090
$105$	8.46440	+	0.999489i	0.826041	+	0.0975402i
$106$	6.75117	−	6.75117i	0.655732	−	0.655732i
$107$	6.27687	−	6.27687i	0.606808	−	0.606808i	−0.335302	−	0.942111i	$-0.608838\pi$
$107$	6.27687	−	6.27687i	0.606808	−	0.606808i	0.942111	+	0.335302i	$0.108838\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	8.01624	−	8.01624i	0.767817	−	0.767817i	−0.209905	−	0.977722i	$-0.567315\pi$
$109$	8.01624	−	8.01624i	0.767817	−	0.767817i	0.977722	+	0.209905i	$0.0673154\pi$
$110$	1.01066	−	8.55899i	0.0963625	−	0.816067i
$111$	−3.71492	−	4.81657i	−0.352605	−	0.457168i
$112$	−2.69527	+	2.69527i	−0.254679	+	0.254679i
$113$	19.1057			1.79732			0.898658	−	0.438650i	$-0.144543\pi$
$113$	19.1057			1.79732			0.898658	+	0.438650i	$0.144543\pi$
$114$	−6.89894			−0.646144
$115$	−14.9317	−	1.76315i	−1.39238	−	0.164415i
$116$	−0.240261	−	0.240261i	−0.0223077	−	0.0223077i
$117$	1.07171			0.0990800
$118$	−1.03632	−	1.03632i	−0.0954014	−	0.0954014i
$119$	8.42597	−	8.42597i	0.772408	−	0.772408i
$120$	−1.75564	+	1.38481i	−0.160268	+	0.126416i
$121$	−3.85554			−0.350504
$122$	9.33589	+	9.33589i	0.845231	+	0.845231i
$123$	6.53622	+	6.53622i	0.589351	+	0.589351i
$124$	7.29610	−	7.29610i	0.655209	−	0.655209i
$125$	−3.86113	+	10.4925i	−0.345350	+	0.938474i
$126$	−2.69527	+	2.69527i	−0.240114	+	0.240114i
$127$	4.73530	−	4.73530i	0.420190	−	0.420190i	−0.465079	−	0.885269i	$-0.653974\pi$
$127$	4.73530	−	4.73530i	0.420190	−	0.420190i	0.885269	+	0.465079i	$0.153974\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.35023	−	6.35023i	−0.559106	−	0.559106i
$130$	−0.281021	+	2.37989i	−0.0246472	+	0.208730i
$131$	10.1880	−	10.1880i	0.890127	−	0.890127i	−0.104408	−	0.994535i	$-0.533295\pi$
$131$	10.1880	−	10.1880i	0.890127	−	0.890127i	0.994535	+	0.104408i	$0.0332947\pi$
$132$	2.72539	+	2.72539i	0.237215	+	0.237215i
$133$		−	26.2966i		−	2.28021i
$134$	0.0813396	−	0.0813396i	0.00702667	−	0.00702667i
$135$	−1.75564	+	1.38481i	−0.151102	+	0.119186i
$136$			3.12620i			0.268070i
$137$	7.57254	−	7.57254i	0.646965	−	0.646965i	−0.305293	−	0.952258i	$-0.598754\pi$
$137$	7.57254	−	7.57254i	0.646965	−	0.646965i	0.952258	+	0.305293i	$0.0987544\pi$
$138$	4.75461	−	4.75461i	0.404739	−	0.404739i
$139$	12.3073			1.04390			0.521948	−	0.852977i	$-0.325206\pi$
$139$	12.3073			1.04390			0.521948	+	0.852977i	$0.325206\pi$
$140$	−5.27849	−	6.69198i	−0.446114	−	0.565575i
$141$			4.43682i			0.373648i
$142$		−	9.73699i		−	0.817110i
$143$	4.13069			0.345426
$144$		−	1.00000i		−	0.0833333i
$145$	0.596534	−	0.470533i	0.0495395	−	0.0390756i
$146$	−3.77094	−	3.77094i	−0.312085	−	0.312085i
$147$	−5.32381	−	5.32381i	−0.439100	−	0.439100i
$148$	−0.778980	+	6.03268i	−0.0640317	+	0.495883i
$149$		−	18.0558i		−	1.47919i	−0.673052	−	0.739596i	$-0.735017\pi$
$149$		−	18.0558i		−	1.47919i	0.673052	−	0.739596i	$-0.264983\pi$
$150$	−2.61482	−	4.26178i	−0.213499	−	0.347973i
$151$		−	0.527274i		−	0.0429089i	−0.999770	−	0.0214545i	$-0.993170\pi$
$151$		−	0.527274i		−	0.0429089i	0.999770	−	0.0214545i	$-0.00682969\pi$
$152$	4.87828	+	4.87828i	0.395681	+	0.395681i
$153$			3.12620i			0.252739i
$154$	−10.3884	+	10.3884i	−0.837118	+	0.837118i
$155$	14.2888	+	18.1152i	1.14771	+	1.45504i
$156$	−0.757816	−	0.757816i	−0.0606738	−	0.0606738i
$157$	−7.56393	+	7.56393i	−0.603668	+	0.603668i	−0.941284	−	0.337616i	$-0.890379\pi$
$157$	−7.56393	+	7.56393i	−0.603668	+	0.603668i	0.337616	+	0.941284i	$0.390379\pi$
$158$	−4.33967	−	4.33967i	−0.345245	−	0.345245i
$159$	−9.54760			−0.757174
$160$	2.22064	+	0.262217i	0.175557	+	0.0207300i
$161$	18.1231	+	18.1231i	1.42830	+	1.42830i
$162$		−	1.00000i		−	0.0785674i
$163$	−16.8338			−1.31852			−0.659262	−	0.751914i	$-0.729131\pi$
$163$	−16.8338			−1.31852			−0.659262	+	0.751914i	$0.729131\pi$
$164$		−	9.24361i		−	0.721805i
$165$	−6.76676	+	5.33747i	−0.526792	+	0.415522i
$166$	5.06491	−	5.06491i	0.393113	−	0.393113i
$167$	−19.7919			−1.53154			−0.765772	−	0.643112i	$-0.777643\pi$
$167$	−19.7919			−1.53154			−0.765772	+	0.643112i	$0.777643\pi$
$168$	3.81169			0.294079
$169$	11.8514			0.911648
$170$	−6.94217	−	0.819742i	−0.532440	−	0.0628714i
$171$	4.87828	+	4.87828i	0.373052	+	0.373052i
$172$			8.98058i			0.684762i
$173$	11.9282	−	11.9282i	0.906886	−	0.906886i	−0.0891340	−	0.996020i	$-0.528410\pi$
$173$	11.9282	−	11.9282i	0.906886	−	0.906886i	0.996020	+	0.0891340i	$0.0284099\pi$
$174$			0.339781i			0.0257587i
$175$	16.2446	−	9.96687i	1.22798	−	0.753425i
$176$		−	3.85429i		−	0.290528i
$177$			1.46558i			0.110160i
$178$	4.92656	−	4.92656i	0.369262	−	0.369262i
$179$	6.14221	+	6.14221i	0.459090	+	0.459090i	0.898357	−	0.439266i	$-0.144762\pi$
$179$	6.14221	+	6.14221i	0.459090	+	0.459090i	−0.439266	+	0.898357i	$0.644762\pi$
$180$	2.22064	+	0.262217i	0.165517	+	0.0195445i
$181$	−11.3224			−0.841587			−0.420793	−	0.907157i	$-0.638248\pi$
$181$	−11.3224			−0.841587			−0.420793	+	0.907157i	$0.638248\pi$
$182$	2.88856	−	2.88856i	0.214114	−	0.214114i
$183$		−	13.2029i		−	0.975989i
$184$	−6.72404			−0.495702
$185$	−13.1921	−	3.31170i	−0.969906	−	0.243481i
$186$	−10.3182			−0.756570
$187$			12.0493i			0.881131i
$188$	3.13731	−	3.13731i	0.228811	−	0.228811i
$189$	3.81169			0.277260
$190$	−12.1121	+	9.55375i	−0.878703	+	0.693102i
$191$	11.4031	+	11.4031i	0.825101	+	0.825101i	0.986834	−	0.161734i	$-0.0517086\pi$
$191$	11.4031	+	11.4031i	0.825101	+	0.825101i	−0.161734	+	0.986834i	$0.551709\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$			25.7217i			1.85149i	0.378150	+	0.925744i	$0.376560\pi$
$193$			25.7217i			1.85149i	−0.378150	+	0.925744i	$0.623440\pi$
$194$		−	2.13394i		−	0.153208i
$195$	1.88155	−	1.48412i	0.134740	−	0.106280i
$196$			7.52901i			0.537786i
$197$	0.296894	−	0.296894i	0.0211528	−	0.0211528i	−0.696451	−	0.717604i	$-0.745239\pi$
$197$	0.296894	−	0.296894i	0.0211528	−	0.0211528i	0.717604	+	0.696451i	$0.245239\pi$
$198$		−	3.85429i		−	0.273912i
$199$	5.41052	+	5.41052i	0.383541	+	0.383541i	0.872376	−	0.488835i	$-0.162578\pi$
$199$	5.41052	+	5.41052i	0.383541	+	0.383541i	−0.488835	+	0.872376i	$0.662578\pi$
$200$	−1.16458	+	4.86248i	−0.0823481	+	0.343830i
$201$	−0.115032			−0.00811370
$202$	−15.9490			−1.12217
$203$	−1.29514			−0.0909010
$204$	2.21056	−	2.21056i	0.154770	−	0.154770i
$205$	20.5267	+	2.42383i	1.43365	+	0.169287i
$206$		−	7.78216i		−	0.542209i
$207$	−6.72404			−0.467353
$208$			1.07171i			0.0743100i
$209$	18.8023	+	18.8023i	1.30058	+	1.30058i
$210$	−0.999489	+	8.46440i	−0.0689713	+	0.584099i
$211$	14.5704			1.00306			0.501532	−	0.865139i	$-0.332770\pi$
$211$	14.5704			1.00306			0.501532	+	0.865139i	$0.332770\pi$
$212$	6.75117	+	6.75117i	0.463672	+	0.463672i
$213$	−6.88509	+	6.88509i	−0.471759	+	0.471759i
$214$	6.27687	+	6.27687i	0.429078	+	0.429078i
$215$	−19.9426	−	2.35486i	−1.36008	−	0.160600i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$		−	39.3300i		−	2.66989i
$218$	8.01624	+	8.01624i	0.542929	+	0.542929i
$219$			5.33291i			0.360365i
$220$	8.55899	+	1.01066i	0.577047	+	0.0681386i
$221$		−	3.35039i		−	0.225372i
$222$	4.81657	−	3.71492i	0.323267	−	0.249329i
$223$	7.68371	+	7.68371i	0.514540	+	0.514540i	0.915914	−	0.401374i	$-0.131467\pi$
$223$	7.68371	+	7.68371i	0.514540	+	0.514540i	−0.401374	+	0.915914i	$0.631467\pi$
$224$	−2.69527	−	2.69527i	−0.180086	−	0.180086i
$225$	−1.16458	+	4.86248i	−0.0776385	+	0.324166i
$226$			19.1057i			1.27089i
$227$	16.0147			1.06293			0.531465	−	0.847080i	$-0.321642\pi$
$227$	16.0147			1.06293			0.531465	+	0.847080i	$0.321642\pi$
$228$		−	6.89894i		−	0.456893i
$229$		−	9.95500i		−	0.657845i	−0.944357	−	0.328923i	$-0.893314\pi$
$229$		−	9.95500i		−	0.657845i	0.944357	−	0.328923i	$-0.106686\pi$
$230$	1.76315	−	14.9317i	0.116259	−	0.984565i
$231$	14.6914			0.966621
$232$	0.240261	−	0.240261i	0.0157739	−	0.0157739i
$233$	16.4078	−	16.4078i	1.07491	−	1.07491i	0.0779551	−	0.996957i	$-0.475161\pi$
$233$	16.4078	−	16.4078i	1.07491	−	1.07491i	0.996957	−	0.0779551i	$-0.0248391\pi$
$234$			1.07171i			0.0700601i
$235$	6.14417	+	7.78948i	0.400802	+	0.508130i
$236$	1.03632	−	1.03632i	0.0674590	−	0.0674590i
$237$			6.13722i			0.398655i
$238$	8.42597	+	8.42597i	0.546175	+	0.546175i
$239$	−16.5390	+	16.5390i	−1.06982	+	1.06982i	−0.0724452	+	0.997372i	$0.523080\pi$
$239$	−16.5390	+	16.5390i	−1.06982	+	1.06982i	−0.997372	+	0.0724452i	$0.976920\pi$
$240$	−1.38481	−	1.75564i	−0.0893894	−	0.113326i
$241$	−9.38903	−	9.38903i	−0.604801	−	0.604801i	0.336782	−	0.941583i	$-0.390662\pi$
$241$	−9.38903	−	9.38903i	−0.604801	−	0.604801i	−0.941583	+	0.336782i	$0.890662\pi$
$242$		−	3.85554i		−	0.247844i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−9.33589	+	9.33589i	−0.597669	+	0.597669i
$245$	−16.7192	−	1.97423i	−1.06815	−	0.126129i
$246$	−6.53622	+	6.53622i	−0.416734	+	0.416734i
$247$	−5.22812	−	5.22812i	−0.332658	−	0.332658i
$248$	7.29610	+	7.29610i	0.463303	+	0.463303i
$249$	−7.16286			−0.453928
$250$	−10.4925	−	3.86113i	−0.663601	−	0.244199i
$251$	−5.58629	+	5.58629i	−0.352603	+	0.352603i	−0.861077	−	0.508474i	$-0.830210\pi$
$251$	−5.58629	+	5.58629i	−0.352603	+	0.352603i	0.508474	+	0.861077i	$0.330210\pi$
$252$	−2.69527	−	2.69527i	−0.169786	−	0.169786i
$253$	−25.9164			−1.62935
$254$	4.73530	+	4.73530i	0.297119	+	0.297119i
$255$	4.32921	+	5.48850i	0.271106	+	0.343703i
$256$	1.00000			0.0625000
$257$	−10.1055			−0.630365			−0.315183	−	0.949031i	$-0.602066\pi$
$257$	−10.1055			−0.630365			−0.315183	+	0.949031i	$0.602066\pi$
$258$	6.35023	−	6.35023i	0.395348	−	0.395348i
$259$	14.1602	+	18.3593i	0.879869	+	1.14079i
$260$	−2.37989	−	0.281021i	−0.147595	−	0.0174282i
$261$	0.240261	−	0.240261i	0.0148718	−	0.0148718i
$262$	10.1880	+	10.1880i	0.629415	+	0.629415i
$263$	−12.6819	+	12.6819i	−0.781998	+	0.781998i	−0.980168	−	0.198170i	$-0.936500\pi$
$263$	−12.6819	+	12.6819i	−0.781998	+	0.781998i	0.198170	+	0.980168i	$0.436500\pi$
$264$	−2.72539	+	2.72539i	−0.167736	+	0.167736i
$265$	−16.7622	+	13.2217i	−1.02969	+	0.812200i
$266$	26.2966			1.61235
$267$	−6.96721			−0.426387
$268$	0.0813396	+	0.0813396i	0.00496861	+	0.00496861i
$269$			26.5570i			1.61921i	0.586978	+	0.809603i	$0.300318\pi$
$269$			26.5570i			1.61921i	−0.586978	+	0.809603i	$0.699682\pi$
$270$	−1.38481	−	1.75564i	−0.0842771	−	0.106845i
$271$	−16.3151			−0.991073			−0.495536	−	0.868587i	$-0.665028\pi$
$271$	−16.3151			−0.991073			−0.495536	+	0.868587i	$0.665028\pi$
$272$	−3.12620			−0.189554
$273$	−4.08504			−0.247238
$274$	7.57254	+	7.57254i	0.457474	+	0.457474i
$275$	−4.48862	+	18.7414i	−0.270674	+	1.13015i
$276$	4.75461	+	4.75461i	0.286194	+	0.286194i
$277$		−	1.82943i		−	0.109920i	−0.998489	−	0.0549600i	$-0.982497\pi$
$277$		−	1.82943i		−	0.109920i	0.998489	−	0.0549600i	$-0.0175031\pi$
$278$			12.3073i			0.738146i
$279$	7.29610	+	7.29610i	0.436806	+	0.436806i
$280$	6.69198	−	5.27849i	0.399922	−	0.315450i
$281$	−8.49578	−	8.49578i	−0.506816	−	0.506816i	0.406732	−	0.913548i	$-0.366668\pi$
$281$	−8.49578	−	8.49578i	−0.506816	−	0.506816i	−0.913548	+	0.406732i	$0.866668\pi$
$282$	−4.43682			−0.264209
$283$	4.60113			0.273509			0.136754	−	0.990605i	$-0.456333\pi$
$283$	4.60113			0.273509			0.136754	+	0.990605i	$0.456333\pi$
$284$	9.73699			0.577784
$285$	15.3201	+	1.80902i	0.907482	+	0.107157i
$286$			4.13069i			0.244253i
$287$	−24.9141	−	24.9141i	−1.47063	−	1.47063i
$288$	1.00000			0.0589256
$289$	−7.22686			−0.425109
$290$	0.470533	+	0.596534i	0.0276307	+	0.0350297i
$291$	−1.50892	+	1.50892i	−0.0884545	+	0.0884545i
$292$	3.77094	−	3.77094i	0.220677	−	0.220677i
$293$	−6.31819	−	6.31819i	−0.369113	−	0.369113i	0.498041	−	0.867154i	$-0.334053\pi$
$293$	−6.31819	−	6.31819i	−0.369113	−	0.369113i	−0.867154	+	0.498041i	$0.834053\pi$
$294$	5.32381	−	5.32381i	0.310491	−	0.310491i
$295$	2.02956	+	2.57304i	0.118166	+	0.149808i
$296$	−6.03268	−	0.778980i	−0.350642	−	0.0452773i
$297$	−2.72539	+	2.72539i	−0.158143	+	0.158143i
$298$	18.0558			1.04595
$299$	7.20624			0.416748
$300$	4.26178	−	2.61482i	0.246054	−	0.150966i
$301$	24.2051	+	24.2051i	1.39516	+	1.39516i
$302$	0.527274			0.0303412
$303$	11.2777	+	11.2777i	0.647885	+	0.647885i
$304$	−4.87828	+	4.87828i	−0.279789	+	0.279789i
$305$	−18.2836	−	23.1797i	−1.04692	−	1.32726i
$306$	−3.12620			−0.178713
$307$	18.6155	+	18.6155i	1.06244	+	1.06244i	0.997916	+	0.0645243i	$0.0205530\pi$
$307$	18.6155	+	18.6155i	1.06244	+	1.06244i	0.0645243	+	0.997916i	$0.479447\pi$
$308$	−10.3884	−	10.3884i	−0.591932	−	0.591932i
$309$	−5.50282	+	5.50282i	−0.313044	+	0.313044i
$310$	−18.1152	+	14.2888i	−1.02887	+	0.811552i
$311$	1.28712	−	1.28712i	0.0729856	−	0.0729856i	−0.669672	−	0.742657i	$-0.733565\pi$
$311$	1.28712	−	1.28712i	0.0729856	−	0.0729856i	0.742657	+	0.669672i	$0.233565\pi$
$312$	0.757816	−	0.757816i	0.0429029	−	0.0429029i
$313$		−	32.0767i		−	1.81308i	−0.422120	−	0.906540i	$-0.638714\pi$
$313$		−	32.0767i		−	1.81308i	0.422120	−	0.906540i	$-0.361286\pi$
$314$	−7.56393	−	7.56393i	−0.426857	−	0.426857i
$315$	6.69198	−	5.27849i	0.377050	−	0.297409i
$316$	4.33967	−	4.33967i	0.244125	−	0.244125i
$317$	−5.14557	−	5.14557i	−0.289004	−	0.289004i	0.547682	−	0.836686i	$-0.315510\pi$
$317$	−5.14557	−	5.14557i	−0.289004	−	0.289004i	−0.836686	+	0.547682i	$0.815510\pi$
$318$		−	9.54760i		−	0.535403i
$319$	0.926036	−	0.926036i	0.0518481	−	0.0518481i
$320$	−0.262217	+	2.22064i	−0.0146584	+	0.124138i
$321$		−	8.87684i		−	0.495457i
$322$	−18.1231	+	18.1231i	−1.00996	+	1.00996i
$323$	15.2505	−	15.2505i	0.848561	−	0.848561i
$324$	1.00000			0.0555556
$325$	1.24809	−	5.21119i	0.0692318	−	0.289065i
$326$		−	16.8338i		−	0.932337i
$327$		−	11.3367i		−	0.626920i
$328$	9.24361			0.510393
$329$		−	16.9118i		−	0.932377i
$330$	−5.33747	−	6.76676i	−0.293818	−	0.372498i
$331$	−8.41827	−	8.41827i	−0.462710	−	0.462710i	0.436833	−	0.899543i	$-0.356100\pi$
$331$	−8.41827	−	8.41827i	−0.462710	−	0.462710i	−0.899543	+	0.436833i	$0.856100\pi$
$332$	5.06491	+	5.06491i	0.277973	+	0.277973i
$333$	−6.03268	−	0.778980i	−0.330589	−	0.0426878i
$334$		−	19.7919i		−	1.08297i
$335$	−0.201955	+	0.159297i	−0.0110340	+	0.00870335i
$336$			3.81169i			0.207945i
$337$	−5.24126	−	5.24126i	−0.285510	−	0.285510i	0.549792	−	0.835302i	$-0.314707\pi$
$337$	−5.24126	−	5.24126i	−0.285510	−	0.285510i	−0.835302	+	0.549792i	$0.814707\pi$
$338$			11.8514i			0.644633i
$339$	13.5098	−	13.5098i	0.733751	−	0.733751i
$340$	0.819742	−	6.94217i	0.0444568	−	0.376492i
$341$	28.1213	+	28.1213i	1.52285	+	1.52285i
$342$	−4.87828	+	4.87828i	−0.263787	+	0.263787i
$343$	1.42581	+	1.42581i	0.0769867	+	0.0769867i
$344$	−8.98058			−0.484200
$345$	−11.8050	+	9.31154i	−0.635561	+	0.501317i
$346$	11.9282	+	11.9282i	0.641265	+	0.641265i
$347$		−	27.4976i		−	1.47615i	−0.674720	−	0.738074i	$-0.735735\pi$
$347$		−	27.4976i		−	1.47615i	0.674720	−	0.738074i	$-0.264265\pi$
$348$	−0.339781			−0.0182142
$349$		−	5.28646i		−	0.282978i	−0.989940	−	0.141489i	$-0.954811\pi$
$349$		−	5.28646i		−	0.282978i	0.989940	−	0.141489i	$-0.0451890\pi$
$350$	9.96687	+	16.2446i	0.532752	+	0.868310i
$351$	0.757816	−	0.757816i	0.0404492	−	0.0404492i
$352$	3.85429			0.205434
$353$	−2.70748			−0.144105			−0.0720523	−	0.997401i	$-0.522955\pi$
$353$	−2.70748			−0.144105			−0.0720523	+	0.997401i	$0.522955\pi$
$354$	−1.46558			−0.0778949
$355$	−2.55320	+	21.6224i	−0.135510	+	1.14760i
$356$	4.92656	+	4.92656i	0.261107	+	0.261107i
$357$		−	11.9161i		−	0.630668i
$358$	−6.14221	+	6.14221i	−0.324626	+	0.324626i
$359$			20.4504i			1.07933i	0.841880	+	0.539665i	$0.181449\pi$
$359$			20.4504i			1.07933i	−0.841880	+	0.539665i	$0.818551\pi$
$360$	−0.262217	+	2.22064i	−0.0138200	+	0.117038i
$361$		−	28.5953i		−	1.50502i
$362$		−	11.3224i		−	0.595092i
$363$	−2.72628	+	2.72628i	−0.143093	+	0.143093i
$364$	2.88856	+	2.88856i	0.151402	+	0.151402i
$365$	7.38509	+	9.36269i	0.386553	+	0.490066i
$366$	13.2029			0.690129
$367$	−0.867537	+	0.867537i	−0.0452851	+	0.0452851i	−0.729387	−	0.684102i	$-0.760194\pi$
$367$	−0.867537	+	0.867537i	−0.0452851	+	0.0452851i	0.684102	+	0.729387i	$0.260194\pi$
$368$		−	6.72404i		−	0.350515i
$369$	9.24361			0.481203
$370$	3.31170	−	13.1921i	0.172167	−	0.685827i
$371$	36.3925			1.88941
$372$		−	10.3182i		−	0.534976i
$373$	−20.6119	+	20.6119i	−1.06725	+	1.06725i	−0.0696765	+	0.997570i	$0.522197\pi$
$373$	−20.6119	+	20.6119i	−1.06725	+	1.06725i	−0.997570	+	0.0696765i	$0.977803\pi$
$374$	−12.0493			−0.623054
$375$	4.68905	+	10.1495i	0.242142	+	0.524119i
$376$	3.13731	+	3.13731i	0.161794	+	0.161794i
$377$	−0.257491	+	0.257491i	−0.0132615	+	0.0132615i
$378$			3.81169i			0.196052i
$379$		−	9.54382i		−	0.490233i	−0.969494	−	0.245117i	$-0.921174\pi$
$379$		−	9.54382i		−	0.490233i	0.969494	−	0.245117i	$-0.0788263\pi$
$380$	−9.55375	−	12.1121i	−0.490097	−	0.621337i
$381$		−	6.69672i		−	0.343083i
$382$	−11.4031	+	11.4031i	−0.583434	+	0.583434i
$383$			5.14097i			0.262691i	0.991337	+	0.131346i	$0.0419298\pi$
$383$			5.14097i			0.262691i	−0.991337	+	0.131346i	$0.958070\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	25.7928	−	20.3448i	1.31452	−	1.03687i
$386$	−25.7217			−1.30920
$387$	−8.98058			−0.456508
$388$	2.13394			0.108334
$389$	13.7109	−	13.7109i	0.695168	−	0.695168i	−0.268196	−	0.963364i	$-0.586428\pi$
$389$	13.7109	−	13.7109i	0.695168	−	0.695168i	0.963364	+	0.268196i	$0.0864276\pi$
$390$	1.48412	+	1.88155i	0.0751516	+	0.0952759i
$391$			21.0207i			1.06306i
$392$	−7.52901			−0.380272
$393$		−	14.4080i		−	0.726786i
$394$	0.296894	+	0.296894i	0.0149573	+	0.0149573i
$395$	8.49891	+	10.7748i	0.427626	+	0.542138i
$396$	3.85429			0.193685
$397$	22.3090	+	22.3090i	1.11966	+	1.11966i	0.991792	+	0.127864i	$0.0408122\pi$
$397$	22.3090	+	22.3090i	1.11966	+	1.11966i	0.127864	+	0.991792i	$0.459188\pi$
$398$	−5.41052	+	5.41052i	−0.271205	+	0.271205i
$399$	−18.5945	−	18.5945i	−0.930890	−	0.930890i
$400$	−4.86248	−	1.16458i	−0.243124	−	0.0582289i
$401$	6.05401	−	6.05401i	0.302323	−	0.302323i	−0.539599	−	0.841922i	$-0.681424\pi$
$401$	6.05401	−	6.05401i	0.302323	−	0.302323i	0.841922	+	0.539599i	$0.181424\pi$
$402$		−	0.115032i		−	0.00573725i
$403$	−7.81933	−	7.81933i	−0.389508	−	0.389508i
$404$		−	15.9490i		−	0.793494i
$405$	−0.262217	+	2.22064i	−0.0130297	+	0.110344i
$406$		−	1.29514i		−	0.0642767i
$407$	−23.2517	−	3.00241i	−1.15254	−	0.148824i
$408$	2.21056	+	2.21056i	0.109439	+	0.109439i
$409$	6.83746	+	6.83746i	0.338091	+	0.338091i	0.855648	−	0.517558i	$-0.173159\pi$
$409$	6.83746	+	6.83746i	0.338091	+	0.338091i	−0.517558	+	0.855648i	$0.673159\pi$
$410$	−2.42383	+	20.5267i	−0.119704	+	1.01374i
$411$		−	10.7092i		−	0.528245i
$412$	7.78216			0.383399
$413$		−	5.58636i		−	0.274887i
$414$		−	6.72404i		−	0.330468i
$415$	−12.5754	+	9.91924i	−0.617304	+	0.486916i
$416$	−1.07171			−0.0525451
$417$	8.70261	−	8.70261i	0.426169	−	0.426169i
$418$	−18.8023	+	18.8023i	−0.919651	+	0.919651i
$419$		−	12.4992i		−	0.610627i	−0.952252	−	0.305314i	$-0.901239\pi$
$419$		−	12.4992i		−	0.610627i	0.952252	−	0.305314i	$-0.0987613\pi$
$420$	−8.46440	−	0.999489i	−0.413020	−	0.0487701i
$421$	1.21803	−	1.21803i	0.0593634	−	0.0593634i	−0.676802	−	0.736165i	$-0.736635\pi$
$421$	1.21803	−	1.21803i	0.0593634	−	0.0593634i	0.736165	+	0.676802i	$0.236635\pi$
$422$			14.5704i			0.709274i
$423$	3.13731	+	3.13731i	0.152541	+	0.152541i
$424$	−6.75117	+	6.75117i	−0.327866	+	0.327866i
$425$	15.2011	+	3.64071i	0.737362	+	0.176600i
$426$	−6.88509	−	6.88509i	−0.333584	−	0.333584i
$427$			50.3255i			2.43542i
$428$	−6.27687	+	6.27687i	−0.303404	+	0.303404i
$429$	2.92084	−	2.92084i	0.141020	−	0.141020i
$430$	2.35486	−	19.9426i	0.113561	−	0.961719i
$431$	−12.0202	+	12.0202i	−0.578993	+	0.578993i	−0.934626	−	0.355633i	$-0.884265\pi$
$431$	−12.0202	+	12.0202i	−0.578993	+	0.578993i	0.355633	+	0.934626i	$0.384265\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−15.2027	−	15.2027i	−0.730596	−	0.730596i	0.240142	−	0.970738i	$-0.422806\pi$
$433$	−15.2027	−	15.2027i	−0.730596	−	0.730596i	−0.970738	+	0.240142i	$0.922806\pi$
$434$	39.3300			1.88790
$435$	0.0890961	−	0.754530i	0.00427183	−	0.0361770i
$436$	−8.01624	+	8.01624i	−0.383908	+	0.383908i
$437$	32.8018	+	32.8018i	1.56912	+	1.56912i
$438$	−5.33291			−0.254816
$439$	3.20813	+	3.20813i	0.153116	+	0.153116i	0.779508	−	0.626392i	$-0.215469\pi$
$439$	3.20813	+	3.20813i	0.153116	+	0.153116i	−0.626392	+	0.779508i	$0.715469\pi$
$440$	−1.01066	+	8.55899i	−0.0481813	+	0.408034i
$441$	−7.52901			−0.358524
$442$	3.35039			0.159362
$443$	−7.74996	+	7.74996i	−0.368211	+	0.368211i	−0.866825	−	0.498613i	$-0.833843\pi$
$443$	−7.74996	+	7.74996i	−0.368211	+	0.368211i	0.498613	+	0.866825i	$0.333843\pi$
$444$	3.71492	+	4.81657i	0.176303	+	0.228584i
$445$	−12.2320	+	9.64830i	−0.579850	+	0.457373i
$446$	−7.68371	+	7.68371i	−0.363834	+	0.363834i
$447$	−12.7674	−	12.7674i	−0.603877	−	0.603877i
$448$	2.69527	−	2.69527i	0.127340	−	0.127340i
$449$	10.4682	−	10.4682i	0.494024	−	0.494024i	−0.415548	−	0.909571i	$-0.636410\pi$
$449$	10.4682	−	10.4682i	0.494024	−	0.494024i	0.909571	+	0.415548i	$0.136410\pi$
$450$	−4.86248	−	1.16458i	−0.229220	−	0.0548987i
$451$	35.6275			1.67764
$452$	−19.1057			−0.898658
$453$	−0.372839	−	0.372839i	−0.0175175	−	0.0175175i
$454$			16.0147i			0.751606i
$455$	−7.17189	+	5.65703i	−0.336223	+	0.265206i
$456$	6.89894			0.323072
$457$	−1.41085			−0.0659970			−0.0329985	−	0.999455i	$-0.510506\pi$
$457$	−1.41085			−0.0659970			−0.0329985	+	0.999455i	$0.510506\pi$
$458$	9.95500			0.465167
$459$	2.21056	+	2.21056i	0.103180	+	0.103180i
$460$	14.9317	+	1.76315i	0.696192	+	0.0822075i
$461$	−17.2878	−	17.2878i	−0.805173	−	0.805173i	0.178726	−	0.983899i	$-0.442802\pi$
$461$	−17.2878	−	17.2878i	−0.805173	−	0.805173i	−0.983899	+	0.178726i	$0.942802\pi$
$462$			14.6914i			0.683504i
$463$		−	27.9587i		−	1.29935i	−0.760212	−	0.649675i	$-0.774905\pi$
$463$		−	27.9587i		−	1.29935i	0.760212	−	0.649675i	$-0.225095\pi$
$464$	0.240261	+	0.240261i	0.0111538	+	0.0111538i
$465$	22.9131	+	2.70561i	1.06257	+	0.125470i
$466$	16.4078	+	16.4078i	0.760078	+	0.760078i
$467$	−25.1108			−1.16199			−0.580995	−	0.813907i	$-0.697336\pi$
$467$	−25.1108			−1.16199			−0.580995	+	0.813907i	$0.697336\pi$
$468$	−1.07171			−0.0495400
$469$	0.438465			0.0202464
$470$	−7.78948	+	6.14417i	−0.359302	+	0.283410i
$471$			10.6970i			0.492893i
$472$	1.03632	+	1.03632i	0.0477007	+	0.0477007i
$473$	−34.6137			−1.59154
$474$	−6.13722			−0.281892
$475$	29.4017	−	18.0394i	1.34904	−	0.827706i
$476$	−8.42597	+	8.42597i	−0.386204	+	0.386204i
$477$	−6.75117	+	6.75117i	−0.309115	+	0.309115i
$478$	−16.5390	−	16.5390i	−0.756475	−	0.756475i
$479$	9.67259	−	9.67259i	0.441952	−	0.441952i	−0.450716	−	0.892668i	$-0.648831\pi$
$479$	9.67259	−	9.67259i	0.441952	−	0.441952i	0.892668	+	0.450716i	$0.148831\pi$
$480$	1.75564	−	1.38481i	0.0801339	−	0.0632078i
$481$	6.46530	+	0.834843i	0.294792	+	0.0380656i
$482$	9.38903	−	9.38903i	0.427659	−	0.427659i
$483$	25.6300			1.16620
$484$	3.85554			0.175252
$485$	−0.559554	+	4.73871i	−0.0254080	+	0.215174i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−28.7468			−1.30264			−0.651321	−	0.758803i	$-0.725785\pi$
$487$	−28.7468			−1.30264			−0.651321	+	0.758803i	$0.725785\pi$
$488$	−9.33589	−	9.33589i	−0.422616	−	0.422616i
$489$	−11.9033	+	11.9033i	−0.538285	+	0.538285i
$490$	1.97423	−	16.7192i	0.0891866	−	0.755297i
$491$	−17.9127			−0.808391			−0.404195	−	0.914673i	$-0.632448\pi$
$491$	−17.9127			−0.808391			−0.404195	+	0.914673i	$0.632448\pi$
$492$	−6.53622	−	6.53622i	−0.294675	−	0.294675i
$493$	−0.751105	−	0.751105i	−0.0338281	−	0.0338281i
$494$	5.22812	−	5.22812i	0.235224	−	0.235224i
$495$	−1.01066	+	8.55899i	−0.0454257	+	0.384698i
$496$	−7.29610	+	7.29610i	−0.327604	+	0.327604i
$497$	26.2439	−	26.2439i	1.17720	−	1.17720i
$498$		−	7.16286i		−	0.320976i
$499$	6.22662	+	6.22662i	0.278742	+	0.278742i	0.832607	−	0.553865i	$-0.186848\pi$
$499$	6.22662	+	6.22662i	0.278742	+	0.278742i	−0.553865	+	0.832607i	$0.686848\pi$
$500$	3.86113	−	10.4925i	0.172675	−	0.469237i
$501$	−13.9950	+	13.9950i	−0.625251	+	0.625251i
$502$	−5.58629	−	5.58629i	−0.249328	−	0.249328i
$503$		−	2.20186i		−	0.0981761i	−0.998794	−	0.0490880i	$-0.984369\pi$
$503$		−	2.20186i		−	0.0981761i	0.998794	−	0.0490880i	$-0.0156315\pi$
$504$	2.69527	−	2.69527i	0.120057	−	0.120057i
$505$	35.4171	+	4.18210i	1.57604	+	0.186101i
$506$		−	25.9164i		−	1.15212i
$507$	8.38023	−	8.38023i	0.372179	−	0.372179i
$508$	−4.73530	+	4.73530i	−0.210095	+	0.210095i
$509$	−4.45209			−0.197335			−0.0986677	−	0.995120i	$-0.531458\pi$
$509$	−4.45209			−0.197335			−0.0986677	+	0.995120i	$0.531458\pi$
$510$	−5.48850	+	4.32921i	−0.243035	+	0.191701i
$511$		−	20.3274i		−	0.899232i
$512$			1.00000i			0.0441942i
$513$	6.89894			0.304595
$514$		−	10.1055i		−	0.445735i
$515$	−2.04061	+	17.2814i	−0.0899201	+	0.761508i
$516$	6.35023	+	6.35023i	0.279553	+	0.279553i
$517$	12.0921	+	12.0921i	0.531809	+	0.531809i
$518$	−18.3593	+	14.1602i	−0.806661	+	0.622161i
$519$		−	16.8690i		−	0.740469i
$520$	0.281021	−	2.37989i	0.0123236	−	0.104365i
$521$			3.61089i			0.158196i	0.996867	+	0.0790979i	$0.0252040\pi$
$521$			3.61089i			0.158196i	−0.996867	+	0.0790979i	$0.974796\pi$
$522$	0.240261	+	0.240261i	0.0105159	+	0.0105159i
$523$		−	30.6225i		−	1.33903i	−0.742799	−	0.669514i	$-0.766502\pi$
$523$		−	30.6225i		−	1.33903i	0.742799	−	0.669514i	$-0.233498\pi$
$524$	−10.1880	+	10.1880i	−0.445063	+	0.445063i
$525$	4.43901	−	18.5343i	0.193734	−	0.808903i
$526$	−12.6819	−	12.6819i	−0.552956	−	0.552956i
$527$	22.8091	−	22.8091i	0.993579	−	0.993579i
$528$	−2.72539	−	2.72539i	−0.118608	−	0.118608i
$529$	−22.2127			−0.965768
$530$	−13.2217	−	16.7622i	−0.574312	−	0.728103i
$531$	1.03632	+	1.03632i	0.0449726	+	0.0449726i
$532$			26.2966i			1.14010i
$533$	−9.90650			−0.429098
$534$		−	6.96721i		−	0.301501i
$535$	−12.2928	−	15.5846i	−0.531463	−	0.673780i
$536$	−0.0813396	+	0.0813396i	−0.00351334	+	0.00351334i
$537$	8.68640			0.374846
$538$	−26.5570			−1.14495
$539$	−29.0190			−1.24994
$540$	1.75564	−	1.38481i	0.0755509	−	0.0595929i
$541$	−28.0745	−	28.0745i	−1.20702	−	1.20702i	−0.971989	−	0.235027i	$-0.924482\pi$
$541$	−28.0745	−	28.0745i	−1.20702	−	1.20702i	−0.235027	−	0.971989i	$-0.575518\pi$
$542$		−	16.3151i		−	0.700794i
$543$	−8.00614	+	8.00614i	−0.343576	+	0.343576i
$544$		−	3.12620i		−	0.134035i
$545$	−15.6992	−	19.9032i	−0.672480	−	0.852559i
$546$		−	4.08504i		−	0.174824i
$547$			20.4389i			0.873904i	0.899485	+	0.436952i	$0.143942\pi$
$547$			20.4389i			0.873904i	−0.899485	+	0.436952i	$0.856058\pi$
$548$	−7.57254	+	7.57254i	−0.323483	+	0.323483i
$549$	−9.33589	−	9.33589i	−0.398446	−	0.398446i
$550$	−18.7414	−	4.48862i	−0.799137	−	0.191395i
$551$	−2.34412			−0.0998631
$552$	−4.75461	+	4.75461i	−0.202370	+	0.202370i
$553$		−	23.3932i		−	0.994780i
$554$	1.82943			0.0777252
$555$	−11.6700	+	6.98653i	−0.495363	+	0.296562i
$556$	−12.3073			−0.521948
$557$		−	39.1876i		−	1.66043i	−0.557443	−	0.830215i	$-0.688217\pi$
$557$		−	39.1876i		−	1.66043i	0.557443	−	0.830215i	$-0.311783\pi$
$558$	−7.29610	+	7.29610i	−0.308868	+	0.308868i
$559$	9.62461			0.407077
$560$	5.27849	+	6.69198i	0.223057	+	0.282788i
$561$	8.52013	+	8.52013i	0.359720	+	0.359720i
$562$	8.49578	−	8.49578i	0.358373	−	0.358373i
$563$		−	15.3734i		−	0.647910i	−0.946073	−	0.323955i	$-0.894987\pi$
$563$		−	15.3734i		−	0.647910i	0.946073	−	0.323955i	$-0.105013\pi$
$564$		−	4.43682i		−	0.186824i
$565$	5.00984	−	42.4270i	0.210766	−	1.78492i
$566$			4.60113i			0.193400i
$567$	2.69527	−	2.69527i	0.113191	−	0.113191i
$568$			9.73699i			0.408555i
$569$	−11.9446	−	11.9446i	−0.500743	−	0.500743i	0.410925	−	0.911669i	$-0.365206\pi$
$569$	−11.9446	−	11.9446i	−0.500743	−	0.500743i	−0.911669	+	0.410925i	$0.865206\pi$
$570$	−1.80902	+	15.3201i	−0.0757713	+	0.641686i
$571$	−19.6843			−0.823762			−0.411881	−	0.911238i	$-0.635128\pi$
$571$	−19.6843			−0.823762			−0.411881	+	0.911238i	$0.635128\pi$
$572$	−4.13069			−0.172713
$573$	16.1264			0.673692
$574$	24.9141	−	24.9141i	1.03989	−	1.03989i
$575$	−7.83066	+	32.6955i	−0.326561	+	1.36350i
$576$			1.00000i			0.0416667i
$577$	43.0027			1.79022			0.895112	−	0.445841i	$-0.147095\pi$
$577$	43.0027			1.79022			0.895112	+	0.445841i	$0.147095\pi$
$578$		−	7.22686i		−	0.300598i
$579$	18.1880	+	18.1880i	0.755867	+	0.755867i
$580$	−0.596534	+	0.470533i	−0.0247697	+	0.0195378i
$581$	27.3026			1.13270
$582$	−1.50892	−	1.50892i	−0.0625468	−	0.0625468i
$583$	−26.0210	+	26.0210i	−1.07768	+	1.07768i
$584$	3.77094	+	3.77094i	0.156042	+	0.156042i
$585$	0.281021	−	2.37989i	0.0116188	−	0.0983964i
$586$	6.31819	−	6.31819i	0.261002	−	0.261002i
$587$		−	2.93901i		−	0.121306i	−0.998159	−	0.0606530i	$-0.980682\pi$
$587$		−	2.93901i		−	0.121306i	0.998159	−	0.0606530i	$-0.0193183\pi$
$588$	5.32381	+	5.32381i	0.219550	+	0.219550i
$589$		−	71.1849i		−	2.93312i
$590$	−2.57304	+	2.02956i	−0.105931	+	0.0835557i
$591$		−	0.419872i		−	0.0172712i
$592$	0.778980	−	6.03268i	0.0320159	−	0.247941i
$593$	−31.5947	−	31.5947i	−1.29744	−	1.29744i	−0.930079	−	0.367359i	$-0.880262\pi$
$593$	−31.5947	−	31.5947i	−1.29744	−	1.29744i	−0.367359	−	0.930079i	$-0.619738\pi$
$594$	−2.72539	−	2.72539i	−0.111824	−	0.111824i
$595$	−16.5016	−	20.9205i	−0.676501	−	0.857656i
$596$			18.0558i			0.739596i
$597$	7.65163			0.313160
$598$			7.20624i			0.294685i
$599$			37.7290i			1.54156i	0.637099	+	0.770782i	$0.280134\pi$
$599$			37.7290i			1.54156i	−0.637099	+	0.770782i	$0.719866\pi$
$600$	2.61482	+	4.26178i	0.106749	+	0.173986i
$601$	−20.0120			−0.816305			−0.408152	−	0.912914i	$-0.633827\pi$
$601$	−20.0120			−0.816305			−0.408152	+	0.912914i	$0.633827\pi$
$602$	−24.2051	+	24.2051i	−0.986527	+	0.986527i
$603$	−0.0813396	+	0.0813396i	−0.00331241	+	0.00331241i
$604$			0.527274i			0.0214545i
$605$	−1.01099	+	8.56177i	−0.0411025	+	0.348085i
$606$	−11.2777	+	11.2777i	−0.458124	+	0.458124i
$607$		−	4.73701i		−	0.192269i	−0.995368	−	0.0961347i	$-0.969352\pi$
$607$		−	4.73701i		−	0.192269i	0.995368	−	0.0961347i	$-0.0306480\pi$
$608$	−4.87828	−	4.87828i	−0.197841	−	0.197841i
$609$	−0.915802	+	0.915802i	−0.0371102	+	0.0371102i
$610$	23.1797	−	18.2836i	0.938517	−	0.740282i
$611$	−3.36229	−	3.36229i	−0.136024	−	0.136024i
$612$		−	3.12620i		−	0.126369i
$613$	−7.31952	+	7.31952i	−0.295633	+	0.295633i	−0.839301	−	0.543668i	$-0.817035\pi$
$613$	−7.31952	+	7.31952i	−0.295633	+	0.295633i	0.543668	+	0.839301i	$0.317035\pi$
$614$	−18.6155	+	18.6155i	−0.751259	+	0.751259i
$615$	16.2285	−	12.8007i	0.654396	−	0.516173i
$616$	10.3884	−	10.3884i	0.418559	−	0.418559i
$617$	9.15306	+	9.15306i	0.368488	+	0.368488i	0.866926	−	0.498437i	$-0.166093\pi$
$617$	9.15306	+	9.15306i	0.368488	+	0.368488i	−0.498437	+	0.866926i	$0.666093\pi$
$618$	−5.50282	−	5.50282i	−0.221356	−	0.221356i
$619$	−19.9520			−0.801939			−0.400970	−	0.916091i	$-0.631327\pi$
$619$	−19.9520			−0.801939			−0.400970	+	0.916091i	$0.631327\pi$
$620$	−14.2888	−	18.1152i	−0.573854	−	0.727522i
$621$	−4.75461	+	4.75461i	−0.190796	+	0.190796i
$622$	1.28712	+	1.28712i	0.0516086	+	0.0516086i
$623$	26.5569			1.06398
$624$	0.757816	+	0.757816i	0.0303369	+	0.0303369i
$625$	22.2875	+	11.3255i	0.891501	+	0.453019i
$626$	32.0767			1.28204
$627$	26.5905			1.06192
$628$	7.56393	−	7.56393i	0.301834	−	0.301834i
$629$	−2.43525	+	18.8594i	−0.0970997	+	0.751972i
$630$	5.27849	+	6.69198i	0.210300	+	0.266615i
$631$	−8.03580	+	8.03580i	−0.319900	+	0.319900i	−0.848729	−	0.528828i	$-0.822631\pi$
$631$	−8.03580	+	8.03580i	−0.319900	+	0.319900i	0.528828	+	0.848729i	$0.322631\pi$
$632$	4.33967	+	4.33967i	0.172623	+	0.172623i
$633$	10.3028	−	10.3028i	0.409499	−	0.409499i
$634$	5.14557	−	5.14557i	0.204357	−	0.204357i
$635$	−9.27372	−	11.7571i	−0.368016	−	0.466565i
$636$	9.54760			0.378587
$637$	8.06894			0.319703
$638$	0.926036	+	0.926036i	0.0366621	+	0.0366621i
$639$			9.73699i			0.385189i
$640$	−2.22064	−	0.262217i	−0.0877785	−	0.0103650i
$641$	−6.64909			−0.262623			−0.131312	−	0.991341i	$-0.541919\pi$
$641$	−6.64909			−0.262623			−0.131312	+	0.991341i	$0.541919\pi$
$642$	8.87684			0.350341
$643$	−18.3325			−0.722963			−0.361481	−	0.932379i	$-0.617729\pi$
$643$	−18.3325			−0.722963			−0.361481	+	0.932379i	$0.617729\pi$
$644$	−18.1231	−	18.1231i	−0.714151	−	0.714151i
$645$	−15.7667	+	12.4364i	−0.620813	+	0.489684i
$646$	15.2505	+	15.2505i	0.600023	+	0.600023i
$647$		−	31.8700i		−	1.25294i	−0.779445	−	0.626470i	$-0.784499\pi$
$647$		−	31.8700i		−	1.25294i	0.779445	−	0.626470i	$-0.215501\pi$
$648$			1.00000i			0.0392837i
$649$	3.99429	+	3.99429i	0.156790	+	0.156790i
$650$	5.21119	+	1.24809i	0.204400	+	0.0489543i
$651$	−27.8105	−	27.8105i	−1.08998	−	1.08998i
$652$	16.8338			0.659262
$653$	−6.13141			−0.239941			−0.119970	−	0.992777i	$-0.538280\pi$
$653$	−6.13141			−0.239941			−0.119970	+	0.992777i	$0.538280\pi$
$654$	11.3367			0.443299
$655$	−19.9524	−	25.2953i	−0.779603	−	0.988368i
$656$			9.24361i			0.360902i
$657$	3.77094	+	3.77094i	0.147118	+	0.147118i
$658$	16.9118			0.659290
$659$	−9.15530			−0.356640			−0.178320	−	0.983973i	$-0.557066\pi$
$659$	−9.15530			−0.356640			−0.178320	+	0.983973i	$0.557066\pi$
$660$	6.76676	−	5.33747i	0.263396	−	0.207761i
$661$	−6.95018	+	6.95018i	−0.270331	+	0.270331i	−0.829233	−	0.558903i	$-0.811223\pi$
$661$	−6.95018	+	6.95018i	−0.270331	+	0.270331i	0.558903	+	0.829233i	$0.311223\pi$
$662$	8.41827	−	8.41827i	0.327185	−	0.327185i
$663$	−2.36909	−	2.36909i	−0.0920077	−	0.0920077i
$664$	−5.06491	+	5.06491i	−0.196557	+	0.196557i
$665$	−58.3953	−	6.89541i	−2.26447	−	0.267393i
$666$	0.778980	−	6.03268i	0.0301849	−	0.233761i
$667$	1.61552	−	1.61552i	0.0625534	−	0.0625534i
$668$	19.7919			0.765772
$669$	10.8664			0.420120
$670$	−0.159297	−	0.201955i	−0.00615420	−	0.00780219i
$671$	−35.9832	−	35.9832i	−1.38912	−	1.38912i
$672$	−3.81169			−0.147039
$673$	10.9734	+	10.9734i	0.422993	+	0.422993i	0.886233	−	0.463240i	$-0.153313\pi$
$673$	10.9734	+	10.9734i	0.422993	+	0.422993i	−0.463240	+	0.886233i	$0.653313\pi$
$674$	5.24126	−	5.24126i	0.201886	−	0.201886i
$675$	2.61482	+	4.26178i	0.100644	+	0.164036i
$676$	−11.8514			−0.455824
$677$	−0.690751	−	0.690751i	−0.0265477	−	0.0265477i	0.693708	−	0.720256i	$-0.255976\pi$
$677$	−0.690751	−	0.690751i	−0.0265477	−	0.0265477i	−0.720256	+	0.693708i	$0.755976\pi$
$678$	13.5098	+	13.5098i	0.518841	+	0.518841i
$679$	5.75155	−	5.75155i	0.220724	−	0.220724i
$680$	6.94217	+	0.819742i	0.266220	+	0.0314357i
$681$	11.3241	−	11.3241i	0.433940	−	0.433940i
$682$	−28.1213	+	28.1213i	−1.07682	+	1.07682i
$683$		−	1.42429i		−	0.0544990i	−0.999629	−	0.0272495i	$-0.991325\pi$
$683$		−	1.42429i		−	0.0544990i	0.999629	−	0.0272495i	$-0.00867486\pi$
$684$	−4.87828	−	4.87828i	−0.186526	−	0.186526i
$685$	−14.8302	−	18.8015i	−0.566634	−	0.718369i
$686$	−1.42581	+	1.42581i	−0.0544378	+	0.0544378i
$687$	−7.03925	−	7.03925i	−0.268564	−	0.268564i
$688$		−	8.98058i		−	0.342381i
$689$	7.23532	−	7.23532i	0.275644	−	0.275644i
$690$	−9.31154	−	11.8050i	−0.354484	−	0.449409i
$691$		−	20.8427i		−	0.792894i	−0.918058	−	0.396447i	$-0.870243\pi$
$691$		−	20.8427i		−	0.792894i	0.918058	−	0.396447i	$-0.129757\pi$
$692$	−11.9282	+	11.9282i	−0.453443	+	0.453443i
$693$	10.3884	−	10.3884i	0.394621	−	0.394621i
$694$	27.4976			1.04379
$695$	3.22719	−	27.3302i	0.122414	−	1.03669i
$696$		−	0.339781i		−	0.0128794i
$697$		−	28.8974i		−	1.09457i
$698$	5.28646			0.200096
$699$		−	23.2042i		−	0.877662i
$700$	−16.2446	+	9.96687i	−0.613988	+	0.376712i
$701$	12.5457	+	12.5457i	0.473846	+	0.473846i	0.903157	−	0.429311i	$-0.141244\pi$
$701$	12.5457	+	12.5457i	0.473846	+	0.473846i	−0.429311	+	0.903157i	$0.641244\pi$
$702$	0.757816	+	0.757816i	0.0286019	+	0.0286019i
$703$	25.6290	+	33.2292i	0.966617	+	1.25326i
$704$			3.85429i			0.145264i
$705$	9.85258	+	1.16341i	0.371070	+	0.0438165i
$706$		−	2.70748i		−	0.101897i
$707$	−42.9870	−	42.9870i	−1.61669	−	1.61669i
$708$		−	1.46558i		−	0.0550800i
$709$	31.0687	−	31.0687i	1.16681	−	1.16681i	0.183856	−	0.982953i	$-0.441142\pi$
$709$	31.0687	−	31.0687i	1.16681	−	1.16681i	0.982953	−	0.183856i	$-0.0588579\pi$
$710$	−21.6224	−	2.55320i	−0.811472	−	0.0958199i
$711$	4.33967	+	4.33967i	0.162750	+	0.162750i
$712$	−4.92656	+	4.92656i	−0.184631	+	0.184631i
$713$	49.0592	+	49.0592i	1.83728	+	1.83728i
$714$	11.9161			0.445950
$715$	1.08314	−	9.17278i	0.0405070	−	0.343043i
$716$	−6.14221	−	6.14221i	−0.229545	−	0.229545i
$717$			23.3896i			0.873502i
$718$	−20.4504			−0.763202
$719$			4.08903i			0.152495i	0.997089	+	0.0762475i	$0.0242939\pi$
$719$			4.08903i			0.152495i	−0.997089	+	0.0762475i	$0.975706\pi$
$720$	−2.22064	−	0.262217i	−0.0827584	−	0.00977224i
$721$	20.9750	−	20.9750i	0.781151	−	0.781151i
$722$	28.5953			1.06421
$723$	−13.2781			−0.493818
$724$	11.3224			0.420793
$725$	−0.888464	−	1.44807i	−0.0329967	−	0.0537799i
$726$	−2.72628	−	2.72628i	−0.101182	−	0.101182i
$727$		−	4.10966i		−	0.152419i	−0.997092	−	0.0762094i	$-0.975718\pi$
$727$		−	4.10966i		−	0.152419i	0.997092	−	0.0762094i	$-0.0242818\pi$
$728$	−2.88856	+	2.88856i	−0.107057	+	0.107057i
$729$			1.00000i			0.0370370i
$730$	−9.36269	+	7.38509i	−0.346529	+	0.273334i
$731$			28.0751i			1.03840i
$732$			13.2029i			0.487995i
$733$	−18.6280	+	18.6280i	−0.688042	+	0.688042i	−0.961799	−	0.273757i	$-0.911734\pi$
$733$	−18.6280	+	18.6280i	−0.688042	+	0.688042i	0.273757	+	0.961799i	$0.411734\pi$
$734$	−0.867537	−	0.867537i	−0.0320214	−	0.0320214i
$735$	−13.2183	+	10.4263i	−0.487563	+	0.384579i
$736$	6.72404			0.247851
$737$	−0.313506	+	0.313506i	−0.0115482	+	0.0115482i
$738$			9.24361i			0.340262i
$739$	−14.2761			−0.525154			−0.262577	−	0.964911i	$-0.584572\pi$
$739$	−14.2761			−0.525154			−0.262577	+	0.964911i	$0.584572\pi$
$740$	13.1921	+	3.31170i	0.484953	+	0.121741i
$741$	−7.39368			−0.271614
$742$			36.3925i			1.33601i
$743$	−16.7892	+	16.7892i	−0.615937	+	0.615937i	−0.944487	−	0.328550i	$-0.893440\pi$
$743$	−16.7892	+	16.7892i	−0.615937	+	0.615937i	0.328550	+	0.944487i	$0.393440\pi$
$744$	10.3182			0.378285
$745$	−40.0955	−	4.73454i	−1.46899	−	0.173460i
$746$	−20.6119	−	20.6119i	−0.754657	−	0.754657i
$747$	−5.06491	+	5.06491i	−0.185315	+	0.185315i
$748$		−	12.0493i		−	0.440566i
$749$			33.8358i			1.23633i
$750$	−10.1495	+	4.68905i	−0.370608	+	0.171220i
$751$			29.4388i			1.07424i	0.843506	+	0.537119i	$0.180487\pi$
$751$			29.4388i			1.07424i	−0.843506	+	0.537119i	$0.819513\pi$
$752$	−3.13731	+	3.13731i	−0.114406	+	0.114406i
$753$			7.90020i			0.287899i
$754$	−0.257491	−	0.257491i	−0.00937728	−	0.00937728i
$755$	−1.17089	−	0.138260i	−0.0426129	−	0.00503180i
$756$	−3.81169			−0.138630
$757$	−9.76824			−0.355033			−0.177516	−	0.984118i	$-0.556806\pi$
$757$	−9.76824			−0.355033			−0.177516	+	0.984118i	$0.556806\pi$
$758$	9.54382			0.346647
$759$	−18.3256	+	18.3256i	−0.665179	+	0.665179i
$760$	12.1121	−	9.55375i	0.439351	−	0.346551i
$761$		−	15.7759i		−	0.571875i	−0.958248	−	0.285938i	$-0.907695\pi$
$761$		−	15.7759i		−	0.571875i	0.958248	−	0.285938i	$-0.0923051\pi$
$762$	6.69672			0.242597
$763$			43.2120i			1.56438i
$764$	−11.4031	−	11.4031i	−0.412550	−	0.412550i
$765$	6.94217	+	0.819742i	0.250995	+	0.0296379i
$766$	−5.14097			−0.185751
$767$	−1.11064	−	1.11064i	−0.0401030	−	0.0401030i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	28.2128	+	28.2128i	1.01738	+	1.01738i	0.999846	+	0.0175316i	$0.00558077\pi$
$769$	28.2128	+	28.2128i	1.01738	+	1.01738i	0.0175316	+	0.999846i	$0.494419\pi$
$770$	20.3448	+	25.7928i	0.733176	+	0.929509i
$771$	−7.14568	+	7.14568i	−0.257345	+	0.257345i
$772$		−	25.7217i		−	0.925744i
$773$	26.4095	+	26.4095i	0.949882	+	0.949882i	0.998803	−	0.0489203i	$-0.0155780\pi$
$773$	26.4095	+	26.4095i	0.949882	+	0.949882i	−0.0489203	+	0.998803i	$0.515578\pi$
$774$		−	8.98058i		−	0.322800i
$775$	43.9740	−	26.9803i	1.57959	−	0.969161i
$776$			2.13394i			0.0766039i
$777$	22.9947	+	2.96923i	0.824931	+	0.106521i
$778$	13.7109	+	13.7109i	0.491558	+	0.491558i
$779$	−45.0929	−	45.0929i	−1.61562	−	1.61562i
$780$	−1.88155	+	1.48412i	−0.0673702	+	0.0531402i
$781$			37.5292i			1.34290i
$782$	−21.0207			−0.751699
$783$		−	0.339781i		−	0.0121428i
$784$		−	7.52901i		−	0.268893i
$785$	14.8134	+	18.7802i	0.528712	+	0.670293i
$786$	14.4080			0.513915
$787$	4.33592	−	4.33592i	0.154559	−	0.154559i	−0.625592	−	0.780151i	$-0.715142\pi$
$787$	4.33592	−	4.33592i	0.154559	−	0.154559i	0.780151	+	0.625592i	$0.215142\pi$
$788$	−0.296894	+	0.296894i	−0.0105764	+	0.0105764i
$789$			17.9349i			0.638498i
$790$	−10.7748	+	8.49891i	−0.383349	+	0.302378i
$791$	−51.4952	+	51.4952i	−1.83096	+	1.83096i
$792$			3.85429i			0.136956i
$793$	10.0054	+	10.0054i	0.355302	+	0.355302i
$794$	−22.3090	+	22.3090i	−0.791716	+	0.791716i
$795$	−2.50354	+	21.2018i	−0.0887914	+	0.751950i
$796$	−5.41052	−	5.41052i	−0.191771	−	0.191771i
$797$		−	0.184397i		−	0.00653168i	−0.999995	−	0.00326584i	$-0.998960\pi$
$797$		−	0.184397i		−	0.00653168i	0.999995	−	0.00326584i	$-0.00103955\pi$
$798$	18.5945	−	18.5945i	0.658239	−	0.658239i
$799$	9.80785	−	9.80785i	0.346977	−	0.346977i
$800$	1.16458	−	4.86248i	0.0411740	−	0.171915i
$801$	−4.92656	+	4.92656i	−0.174072	+	0.174072i
$802$	6.05401	+	6.05401i	0.213775	+	0.213775i
$803$	14.5343	+	14.5343i	0.512903	+	0.512903i
$804$	0.115032			0.00405685
$805$	44.9971	−	35.4927i	1.58594	−	1.25095i
$806$	7.81933	−	7.81933i	0.275424	−	0.275424i
$807$	18.7786	+	18.7786i	0.661038	+	0.661038i
$808$	15.9490			0.561085
$809$	18.7803	+	18.7803i	0.660281	+	0.660281i	0.955446	−	0.295165i	$-0.0953746\pi$
$809$	18.7803	+	18.7803i	0.660281	+	0.660281i	−0.295165	+	0.955446i	$0.595375\pi$
$810$	−2.22064	−	0.262217i	−0.0780253	−	0.00921335i
$811$	−46.9131			−1.64734			−0.823670	−	0.567069i	$-0.808077\pi$
$811$	−46.9131			−1.64734			−0.823670	+	0.567069i	$0.808077\pi$
$812$	1.29514			0.0454505
$813$	−11.5365	+	11.5365i	−0.404604	+	0.404604i
$814$	3.00241	−	23.2517i	0.105235	−	0.814971i
$815$	−4.41410	+	37.3818i	−0.154619	+	1.30943i
$816$	−2.21056	+	2.21056i	−0.0773851	+	0.0773851i
$817$	43.8098	+	43.8098i	1.53271	+	1.53271i
$818$	−6.83746	+	6.83746i	−0.239066	+	0.239066i
$819$	−2.88856	+	2.88856i	−0.100935	+	0.100935i
$820$	−20.5267	−	2.42383i	−0.716824	−	0.0846437i
$821$	19.7666			0.689859			0.344930	−	0.938629i	$-0.387903\pi$
$821$	19.7666			0.689859			0.344930	+	0.938629i	$0.387903\pi$
$822$	10.7092			0.373526
$823$	11.0130	+	11.0130i	0.383889	+	0.383889i	0.872501	−	0.488612i	$-0.162497\pi$
$823$	11.0130	+	11.0130i	0.383889	+	0.383889i	−0.488612	+	0.872501i	$0.662497\pi$
$824$			7.78216i			0.271104i
$825$	10.0783	+	16.4261i	0.350880	+	0.571884i
$826$	5.58636			0.194374
$827$	52.5723			1.82812			0.914059	−	0.405581i	$-0.132931\pi$
$827$	52.5723			1.82812			0.914059	+	0.405581i	$0.132931\pi$
$828$	6.72404			0.233676
$829$	34.5891	+	34.5891i	1.20133	+	1.20133i	0.973762	+	0.227568i	$0.0730773\pi$
$829$	34.5891	+	34.5891i	1.20133	+	1.20133i	0.227568	+	0.973762i	$0.426923\pi$
$830$	−9.91924	−	12.5754i	−0.344302	−	0.436500i
$831$	−1.29360	−	1.29360i	−0.0448747	−	0.0448747i
$832$		−	1.07171i		−	0.0371550i
$833$			23.5372i			0.815516i
$834$	8.70261	+	8.70261i	0.301347	+	0.301347i
$835$	−5.18977	+	43.9507i	−0.179599	+	1.52098i
$836$	−18.8023	−	18.8023i	−0.650292	−	0.650292i
$837$	10.3182			0.356651
$838$	12.4992			0.431779
$839$	−16.5268			−0.570568			−0.285284	−	0.958443i	$-0.592088\pi$
$839$	−16.5268			−0.570568			−0.285284	+	0.958443i	$0.592088\pi$
$840$	0.999489	−	8.46440i	0.0344857	−	0.292050i
$841$		−	28.8845i		−	0.996019i
$842$	1.21803	+	1.21803i	0.0419763	+	0.0419763i
$843$	−12.0148			−0.413813
$844$	−14.5704			−0.501532
$845$	3.10764	−	26.3178i	0.106906	−	0.905358i
$846$	−3.13731	+	3.13731i	−0.107863	+	0.107863i
$847$	10.3917	−	10.3917i	0.357064	−	0.357064i
$848$	−6.75117	−	6.75117i	−0.231836	−	0.231836i
$849$	3.25349	−	3.25349i	0.111660	−	0.111660i
$850$	−3.64071	+	15.2011i	−0.124875	+	0.521394i
$851$	−40.5639	−	5.23789i	−1.39051	−	0.179552i
$852$	6.88509	−	6.88509i	0.235879	−	0.235879i
$853$	−20.2197			−0.692309			−0.346155	−	0.938177i	$-0.612513\pi$
$853$	−20.2197			−0.692309			−0.346155	+	0.938177i	$0.612513\pi$
$854$	−50.3255			−1.72210
$855$	12.1121	−	9.55375i	0.414224	−	0.326731i
$856$	−6.27687	−	6.27687i	−0.214539	−	0.214539i
$857$	−26.0449			−0.889675			−0.444838	−	0.895611i	$-0.646739\pi$
$857$	−26.0449			−0.889675			−0.444838	+	0.895611i	$0.646739\pi$
$858$	2.92084	+	2.92084i	0.0997159	+	0.0997159i
$859$	−5.92987	+	5.92987i	−0.202324	+	0.202324i	−0.800995	−	0.598671i	$-0.795696\pi$
$859$	−5.92987	+	5.92987i	−0.202324	+	0.202324i	0.598671	+	0.800995i	$0.295696\pi$
$860$	19.9426	+	2.35486i	0.680038	+	0.0802999i
$861$	−35.2338			−1.20076
$862$	−12.0202	−	12.0202i	−0.409410	−	0.409410i
$863$	−20.9158	−	20.9158i	−0.711980	−	0.711980i	0.254969	−	0.966949i	$-0.417935\pi$
$863$	−20.9158	−	20.9158i	−0.711980	−	0.711980i	−0.966949	+	0.254969i	$0.917935\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−23.3605	−	29.6161i	−0.794281	−	1.00698i
$866$	15.2027	−	15.2027i	0.516609	−	0.516609i
$867$	−5.11016	+	5.11016i	−0.173550	+	0.173550i
$868$			39.3300i			1.33495i
$869$	16.7263	+	16.7263i	0.567402	+	0.567402i
$870$	0.754530	+	0.0890961i	0.0255810	+	0.00302064i
$871$	0.0871728	−	0.0871728i	0.00295374	−	0.00295374i
$872$	−8.01624	−	8.01624i	−0.271464	−	0.271464i
$873$			2.13394i			0.0722228i
$874$	−32.8018	+	32.8018i	−1.10954	+	1.10954i
$875$	−17.8732	−	38.6869i	−0.604226	−	1.30785i
$876$		−	5.33291i		−	0.180182i
$877$	5.35557	−	5.35557i	0.180845	−	0.180845i	−0.610879	−	0.791724i	$-0.709184\pi$
$877$	5.35557	−	5.35557i	0.180845	−	0.180845i	0.791724	+	0.610879i	$0.209184\pi$
$878$	−3.20813	+	3.20813i	−0.108269	+	0.108269i
$879$	−8.93527			−0.301379
$880$	−8.55899	−	1.01066i	−0.288523	−	0.0340693i
$881$		−	7.99622i		−	0.269400i	−0.990886	−	0.134700i	$-0.956993\pi$
$881$		−	7.99622i		−	0.269400i	0.990886	−	0.134700i	$-0.0430070\pi$
$882$		−	7.52901i		−	0.253515i
$883$	−25.8732			−0.870704			−0.435352	−	0.900260i	$-0.643376\pi$
$883$	−25.8732			−0.870704			−0.435352	+	0.900260i	$0.643376\pi$
$884$			3.35039i			0.112686i
$885$	3.25453	+	0.384300i	0.109400	+	0.0129181i
$886$	−7.74996	−	7.74996i	−0.260365	−	0.260365i
$887$	24.7209	+	24.7209i	0.830045	+	0.830045i	0.987523	−	0.157478i	$-0.0503362\pi$
$887$	24.7209	+	24.7209i	0.830045	+	0.830045i	−0.157478	+	0.987523i	$0.550336\pi$
$888$	−4.81657	+	3.71492i	−0.161633	+	0.124665i
$889$			25.5258i			0.856109i
$890$	−9.64830	−	12.2320i	−0.323412	−	0.410016i
$891$			3.85429i			0.129124i
$892$	−7.68371	−	7.68371i	−0.257270	−	0.257270i
$893$		−	30.6093i		−	1.02430i
$894$	12.7674	−	12.7674i	0.427006	−	0.427006i
$895$	15.2502	−	12.0291i	0.509759	−	0.402087i
$896$	2.69527	+	2.69527i	0.0900428	+	0.0900428i
$897$	5.09558	−	5.09558i	0.170137	−	0.170137i
$898$	10.4682	+	10.4682i	0.349328	+	0.349328i
$899$	−3.50594			−0.116930
$900$	1.16458	−	4.86248i	0.0388193	−	0.162083i
$901$	21.1055	+	21.1055i	0.703127	+	0.703127i
$902$			35.6275i			1.18627i
$903$	34.2312			1.13914
$904$		−	19.1057i		−	0.635447i
$905$	−2.96892	+	25.1430i	−0.0986902	+	0.835780i
$906$	0.372839	−	0.372839i	0.0123867	−	0.0123867i
$907$	−59.2927			−1.96878			−0.984392	−	0.175992i	$-0.943687\pi$
$907$	−59.2927			−1.96878			−0.984392	+	0.175992i	$0.943687\pi$
$908$	−16.0147			−0.531465
$909$	15.9490			0.528996
$910$	−5.65703	−	7.17189i	−0.187529	−	0.237746i
$911$	2.95948	+	2.95948i	0.0980518	+	0.0980518i	0.754431	−	0.656379i	$-0.227913\pi$
$911$	2.95948	+	2.95948i	0.0980518	+	0.0980518i	−0.656379	+	0.754431i	$0.727913\pi$
$912$			6.89894i			0.228447i
$913$	−19.5216	+	19.5216i	−0.646071	+	0.646071i
$914$		−	1.41085i		−	0.0466669i
$915$	−29.3190	−	3.46203i	−0.969255	−	0.114451i
$916$			9.95500i			0.328923i
$917$			54.9187i			1.81358i
$918$	−2.21056	+	2.21056i	−0.0729593	+	0.0729593i
$919$	8.84725	+	8.84725i	0.291844	+	0.291844i	0.837808	−	0.545964i	$-0.183837\pi$
$919$	8.84725	+	8.84725i	0.291844	+	0.291844i	−0.545964	+	0.837808i	$0.683837\pi$
$920$	−1.76315	+	14.9317i	−0.0581295	+	0.492282i
$921$	26.3262			0.867479
$922$	17.2878	−	17.2878i	0.569343	−	0.569343i
$923$		−	10.4353i		−	0.343481i
$924$	−14.6914			−0.483310
$925$	−10.8133	+	28.4266i	−0.355539	+	0.934661i
$926$	27.9587			0.918779
$927$			7.78216i			0.255600i
$928$	−0.240261	+	0.240261i	−0.00788696	+	0.00788696i
$929$	20.1987			0.662699			0.331350	−	0.943508i	$-0.392496\pi$
$929$	20.1987			0.662699			0.331350	+	0.943508i	$0.392496\pi$
$930$	−2.70561	+	22.9131i	−0.0887206	+	0.751350i
$931$	36.7286	+	36.7286i	1.20373	+	1.20373i
$932$	−16.4078	+	16.4078i	−0.537456	+	0.537456i
$933$		−	1.82026i		−	0.0595925i
$934$		−	25.1108i		−	0.821651i
$935$	26.7571	+	3.15952i	0.875052	+	0.103327i
$936$		−	1.07171i		−	0.0350301i
$937$	−4.29731	+	4.29731i	−0.140387	+	0.140387i	−0.773808	−	0.633421i	$-0.781650\pi$
$937$	−4.29731	+	4.29731i	−0.140387	+	0.140387i	0.633421	+	0.773808i	$0.281650\pi$
$938$			0.438465i			0.0143164i
$939$	−22.6816	−	22.6816i	−0.740187	−	0.740187i
$940$	−6.14417	−	7.78948i	−0.200401	−	0.254065i
$941$	−28.1989			−0.919257			−0.459628	−	0.888111i	$-0.652017\pi$
$941$	−28.1989			−0.919257			−0.459628	+	0.888111i	$0.652017\pi$
$942$	−10.6970			−0.348528
$943$	62.1544			2.02402
$944$	−1.03632	+	1.03632i	−0.0337295	+	0.0337295i
$945$	0.999489	−	8.46440i	0.0325134	−	0.275347i
$946$		−	34.6137i		−	1.12539i
$947$	−16.9403			−0.550486			−0.275243	−	0.961375i	$-0.588758\pi$
$947$	−16.9403			−0.550486			−0.275243	+	0.961375i	$0.588758\pi$
$948$		−	6.13722i		−	0.199328i
$949$	−4.04136	−	4.04136i	−0.131188	−	0.131188i
$950$	18.0394	+	29.4017i	0.585277	+	0.953918i
$951$	−7.27694			−0.235971
$952$	−8.42597	−	8.42597i	−0.273087	−	0.273087i
$953$	−7.06463	+	7.06463i	−0.228846	+	0.228846i	−0.812210	−	0.583365i	$-0.801736\pi$
$953$	−7.06463	+	7.06463i	−0.228846	+	0.228846i	0.583365	+	0.812210i	$0.301736\pi$
$954$	−6.75117	−	6.75117i	−0.218577	−	0.218577i
$955$	28.3123	−	22.3321i	0.916165	−	0.722651i
$956$	16.5390	−	16.5390i	0.534909	−	0.534909i
$957$		−	1.30961i		−	0.0423338i
$958$	9.67259	+	9.67259i	0.312507	+	0.312507i
$959$			40.8201i			1.31815i
$960$	1.38481	+	1.75564i	0.0446947	+	0.0566632i
$961$		−	75.4661i		−	2.43439i
$962$	−0.834843	+	6.46530i	−0.0269164	+	0.208450i
$963$	−6.27687	−	6.27687i	−0.202269	−	0.202269i
$964$	9.38903	+	9.38903i	0.302400	+	0.302400i
$965$	57.1186	+	6.74466i	1.83871	+	0.217118i
$966$			25.6300i			0.824630i
$967$	26.0501			0.837716			0.418858	−	0.908052i	$-0.362431\pi$
$967$	26.0501			0.837716			0.418858	+	0.908052i	$0.362431\pi$
$968$			3.85554i			0.123922i
$969$		−	21.5675i		−	0.692847i
$970$	−4.73871	−	0.559554i	−0.152151	−	0.0179662i
$971$	21.0115			0.674292			0.337146	−	0.941452i	$-0.390538\pi$
$971$	21.0115			0.674292			0.337146	+	0.941452i	$0.390538\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−33.1717	+	33.1717i	−1.06344	+	1.06344i
$974$		−	28.7468i		−	0.921106i
$975$	−2.80233	−	4.56740i	−0.0897465	−	0.146274i
$976$	9.33589	−	9.33589i	0.298834	−	0.298834i
$977$			11.5254i			0.368730i	0.982858	+	0.184365i	$0.0590228\pi$
$977$			11.5254i			0.368730i	−0.982858	+	0.184365i	$0.940977\pi$
$978$	−11.9033	−	11.9033i	−0.380625	−	0.380625i
$979$	−18.9884	+	18.9884i	−0.606872	+	0.606872i
$980$	16.7192	+	1.97423i	0.534076	+	0.0630645i
$981$	−8.01624	−	8.01624i	−0.255939	−	0.255939i
$982$		−	17.9127i		−	0.571619i
$983$	28.2941	−	28.2941i	0.902442	−	0.902442i	−0.0932046	−	0.995647i	$-0.529711\pi$
$983$	28.2941	−	28.2941i	0.902442	−	0.902442i	0.995647	+	0.0932046i	$0.0297111\pi$
$984$	6.53622	−	6.53622i	0.208367	−	0.208367i
$985$	−0.581444	−	0.737146i	−0.0185264	−	0.0234874i
$986$	0.751105	−	0.751105i	0.0239201	−	0.0239201i
$987$	−11.9584	−	11.9584i	−0.380641	−	0.380641i
$988$	5.22812	+	5.22812i	0.166329	+	0.166329i
$989$	−60.3857			−1.92015
$990$	−8.55899	−	1.01066i	−0.272022	−	0.0321208i
$991$	−3.63262	+	3.63262i	−0.115394	+	0.115394i	−0.762446	−	0.647052i	$-0.776002\pi$
$991$	−3.63262	+	3.63262i	−0.115394	+	0.115394i	0.647052	+	0.762446i	$0.276002\pi$
$992$	−7.29610	−	7.29610i	−0.231651	−	0.231651i
$993$	−11.9052			−0.377801
$994$	26.2439	+	26.2439i	0.832405	+	0.832405i
$995$	13.4335	−	10.5961i	0.425872	−	0.335918i
$996$	7.16286			0.226964
$997$	−55.1711			−1.74729			−0.873644	−	0.486567i	$-0.838249\pi$
$997$	−55.1711			−1.74729			−0.873644	+	0.486567i	$0.838249\pi$
$998$	−6.22662	+	6.22662i	−0.197100	+	0.197100i
$999$	−4.81657	+	3.71492i	−0.152389	+	0.117535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.18	✓	36
5.2	odd	4		1110.2.o.a.487.2	yes	36
37.31	odd	4		1110.2.o.a.253.2	yes	36
185.142	even	4	inner	1110.2.l.a.697.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.18	✓	36	1.1	even	1	trivial
1110.2.l.a.697.18	yes	36	185.142	even	4	inner
1110.2.o.a.253.2	yes	36	37.31	odd	4
1110.2.o.a.487.2	yes	36	5.2	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.262217 - 2.22064i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 + 2.69527i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.262217 - 2.22064i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 + 2.69527i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.22064 + 0.262217i) q^{10} -3.85429i q^{11} +(-0.707107 + 0.707107i) q^{12} +1.07171i q^{13} +(-2.69527 - 2.69527i) q^{14} +(-1.38481 - 1.75564i) q^{15} +1.00000 q^{16} -3.12620 q^{17} +1.00000 q^{18} +(-4.87828 + 4.87828i) q^{19} +(-0.262217 + 2.22064i) q^{20} +3.81169i q^{21} +3.85429 q^{22} -6.72404i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.86248 - 1.16458i) q^{25} -1.07171 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.69527 - 2.69527i) q^{28} +(0.240261 + 0.240261i) q^{29} +(1.75564 - 1.38481i) q^{30} +(-7.29610 + 7.29610i) q^{31} +1.00000i q^{32} +(-2.72539 - 2.72539i) q^{33} -3.12620i q^{34} +(5.27849 + 6.69198i) q^{35} +1.00000i q^{36} +(0.778980 - 6.03268i) q^{37} +(-4.87828 - 4.87828i) q^{38} +(0.757816 + 0.757816i) q^{39} +(-2.22064 - 0.262217i) q^{40} +9.24361i q^{41} -3.81169 q^{42} -8.98058i q^{43} +3.85429i q^{44} +(-2.22064 - 0.262217i) q^{45} +6.72404 q^{46} +(-3.13731 + 3.13731i) q^{47} +(0.707107 - 0.707107i) q^{48} -7.52901i q^{49} +(1.16458 - 4.86248i) q^{50} +(-2.21056 + 2.21056i) q^{51} -1.07171i q^{52} +(-6.75117 - 6.75117i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-8.55899 - 1.01066i) q^{55} +(2.69527 + 2.69527i) q^{56} +6.89894i q^{57} +(-0.240261 + 0.240261i) q^{58} +(-1.03632 + 1.03632i) q^{59} +(1.38481 + 1.75564i) q^{60} +(9.33589 - 9.33589i) q^{61} +(-7.29610 - 7.29610i) q^{62} +(2.69527 + 2.69527i) q^{63} -1.00000 q^{64} +(2.37989 + 0.281021i) q^{65} +(2.72539 - 2.72539i) q^{66} +(-0.0813396 - 0.0813396i) q^{67} +3.12620 q^{68} +(-4.75461 - 4.75461i) q^{69} +(-6.69198 + 5.27849i) q^{70} -9.73699 q^{71} -1.00000 q^{72} +(-3.77094 + 3.77094i) q^{73} +(6.03268 + 0.778980i) q^{74} +(-4.26178 + 2.61482i) q^{75} +(4.87828 - 4.87828i) q^{76} +(10.3884 + 10.3884i) q^{77} +(-0.757816 + 0.757816i) q^{78} +(-4.33967 + 4.33967i) q^{79} +(0.262217 - 2.22064i) q^{80} -1.00000 q^{81} -9.24361 q^{82} +(-5.06491 - 5.06491i) q^{83} -3.81169i q^{84} +(-0.819742 + 6.94217i) q^{85} +8.98058 q^{86} +0.339781 q^{87} -3.85429 q^{88} +(-4.92656 - 4.92656i) q^{89} +(0.262217 - 2.22064i) q^{90} +(-2.88856 - 2.88856i) q^{91} +6.72404i q^{92} +10.3182i q^{93} +(-3.13731 - 3.13731i) q^{94} +(9.55375 + 12.1121i) q^{95} +(0.707107 + 0.707107i) q^{96} -2.13394 q^{97} +7.52901 q^{98} -3.85429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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