LMFDB - Embedded newform 1110.2.o.a.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.2
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−2.22064	−	0.262217i	−0.993100	−	0.117267i
$5$	−2.22064	−	0.262217i	−0.993100	−	0.117267i
$6$	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	$0.993985\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	2.22064	+	0.262217i	0.702228	+	0.0829202i
$11$			3.85429i			1.16211i	0.813864	+	0.581056i	$0.197360\pi$
$11$			3.85429i			1.16211i	−0.813864	+	0.581056i	$0.802640\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.07171			0.297240			0.148620	−	0.988894i	$-0.452517\pi$
$13$	1.07171			0.297240			0.148620	+	0.988894i	$0.452517\pi$
$14$	2.69527	−	2.69527i	0.720342	−	0.720342i
$15$	1.75564	−	1.38481i	0.453306	−	0.357558i
$16$	1.00000			0.250000
$17$			3.12620i			0.758216i	0.925353	+	0.379108i	$0.123769\pi$
$17$			3.12620i			0.758216i	−0.925353	+	0.379108i	$0.876231\pi$
$18$			1.00000i			0.235702i
$19$	4.87828	+	4.87828i	1.11916	+	1.11916i	0.991866	+	0.127289i	$0.0406277\pi$
$19$	4.87828	+	4.87828i	1.11916	+	1.11916i	0.127289	+	0.991866i	$0.459372\pi$
$20$	−2.22064	−	0.262217i	−0.496550	−	0.0586334i
$21$		−	3.81169i		−	0.831780i
$22$		−	3.85429i		−	0.821737i
$23$	−6.72404			−1.40206			−0.701029	−	0.713133i	$-0.747276\pi$
$23$	−6.72404			−1.40206			−0.701029	+	0.713133i	$0.747276\pi$
$24$	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	$-0.760044\pi$
$29$	−0.240261	+	0.240261i	−0.0446154	+	0.0446154i	0.684447	+	0.729063i	$0.260044\pi$
$30$	−1.75564	+	1.38481i	−0.320535	+	0.252831i
$31$	−7.29610	−	7.29610i	−1.31042	−	1.31042i	−0.921106	−	0.389312i	$-0.872713\pi$
$31$	−7.29610	−	7.29610i	−1.31042	−	1.31042i	−0.389312	−	0.921106i	$-0.627287\pi$
$32$	−1.00000			−0.176777
$33$	−2.72539	−	2.72539i	−0.474430	−	0.474430i
$34$		−	3.12620i		−	0.536139i
$35$	6.69198	−	5.27849i	1.13115	−	0.892227i
$36$		−	1.00000i		−	0.166667i
$37$	6.03268	−	0.778980i	0.991766	−	0.128063i
$37$	6.03268	−	0.778980i	0.991766	−	0.128063i
$38$	−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	$-0.743313\pi$
$41$		−	9.24361i		−	1.44361i	0.692097	−	0.721805i	$-0.256687\pi$
$42$			3.81169i			0.588157i
$43$	−8.98058			−1.36952			−0.684762	−	0.728766i	$-0.740094\pi$
$43$	−8.98058			−1.36952			−0.684762	+	0.728766i	$0.740094\pi$
$44$			3.85429i			0.581056i
$45$	−0.262217	+	2.22064i	−0.0390890	+	0.331033i
$46$	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
$50$	−4.86248	−	1.16458i	−0.687659	−	0.164696i
$51$	−2.21056	−	2.21056i	−0.309540	−	0.309540i
$52$	1.07171			0.148620
$53$	−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
$55$	1.01066	−	8.55899i	0.136277	−	1.15409i
$56$	2.69527	−	2.69527i	0.360171	−	0.360171i
$57$	−6.89894			−0.913786
$58$	0.240261	−	0.240261i	0.0315478	−	0.0315478i
$59$	1.03632	+	1.03632i	0.134918	+	0.134918i	0.771341	−	0.636423i	$-0.219587\pi$
$59$	1.03632	+	1.03632i	0.134918	+	0.134918i	−0.636423	+	0.771341i	$0.719587\pi$
$60$	1.75564	−	1.38481i	0.226653	−	0.178779i
$61$	9.33589	+	9.33589i	1.19534	+	1.19534i	0.975547	+	0.219791i	$0.0705375\pi$
$61$	9.33589	+	9.33589i	1.19534	+	1.19534i	0.219791	+	0.975547i	$0.429463\pi$
$62$	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	0.712058	−	0.702121i	$-0.247763\pi$
$67$	0.0813396	+	0.0813396i	0.00993722	+	0.00993722i	−0.702121	+	0.712058i	$0.747763\pi$
$68$			3.12620i			0.379108i
$69$	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	$0.696082\pi$
$72$			1.00000i			0.117851i
$73$	3.77094	−	3.77094i	0.441355	−	0.441355i	−0.451112	−	0.892467i	$-0.648973\pi$
$73$	3.77094	−	3.77094i	0.441355	−	0.441355i	0.892467	+	0.451112i	$0.148973\pi$
$74$	−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	$-0.137796\pi$
$79$	4.33967	+	4.33967i	0.488251	+	0.488251i	−0.419503	+	0.907754i	$0.637796\pi$
$80$	−2.22064	−	0.262217i	−0.248275	−	0.0293167i
$81$	−1.00000			−0.111111
$82$			9.24361i			1.02079i
$83$	−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
$87$		−	0.339781i		−	0.0364283i
$88$		−	3.85429i		−	0.410869i
$89$	4.92656	−	4.92656i	0.522215	−	0.522215i	−0.396025	−	0.918240i	$-0.629611\pi$
$89$	4.92656	−	4.92656i	0.522215	−	0.522215i	0.918240	+	0.396025i	$0.129611\pi$
$90$	0.262217	−	2.22064i	0.0276401	−	0.234076i
$91$	−2.88856	+	2.88856i	−0.302804	+	0.302804i
$92$	−6.72404			−0.701029
$93$	10.3182			1.06995
$94$	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
$97$			2.13394i			0.216668i	0.994115	+	0.108334i	$0.0345517\pi$
$97$			2.13394i			0.216668i	−0.994115	+	0.108334i	$0.965448\pi$
$98$			7.52901i			0.760544i
$99$	3.85429			0.387371
$100$	4.86248	+	1.16458i	0.486248	+	0.116458i
$101$		−	15.9490i		−	1.58699i	−0.608578	−	0.793494i	$-0.708260\pi$
$101$		−	15.9490i		−	1.58699i	0.608578	−	0.793494i	$-0.291740\pi$
$102$	2.21056	+	2.21056i	0.218878	+	0.218878i
$103$		−	7.78216i		−	0.766799i	−0.923583	−	0.383399i	$-0.874753\pi$
$103$		−	7.78216i		−	0.766799i	0.923583	−	0.383399i	$-0.125247\pi$
$104$	−1.07171			−0.105090
$105$	−0.999489	+	8.46440i	−0.0975402	+	0.826041i
$106$	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	$-0.432685\pi$
$109$	−8.01624	−	8.01624i	−0.767817	−	0.767817i	−0.977722	+	0.209905i	$0.932685\pi$
$110$	−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
$113$			19.1057i			1.79732i	0.438650	+	0.898658i	$0.355457\pi$
$113$			19.1057i			1.79732i	−0.438650	+	0.898658i	$0.644543\pi$
$114$	6.89894			0.646144
$115$	14.9317	+	1.76315i	1.39238	+	0.164415i
$116$	−0.240261	+	0.240261i	−0.0223077	+	0.0223077i
$117$		−	1.07171i		−	0.0990800i
$118$	−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
$125$	−10.4925	−	3.86113i	−0.938474	−	0.345350i
$126$	−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	$0.153974\pi$
$128$	−1.00000			−0.0883883
$129$	6.35023	−	6.35023i	0.559106	−	0.559106i
$130$	2.37989	+	0.281021i	0.208730	+	0.0246472i
$131$	10.1880	+	10.1880i	0.890127	+	0.890127i	0.994535	−	0.104408i	$-0.0332947\pi$
$131$	10.1880	+	10.1880i	0.890127	+	0.890127i	−0.104408	+	0.994535i	$0.533295\pi$
$132$	−2.72539	−	2.72539i	−0.237215	−	0.237215i
$133$	−26.2966			−2.28021
$134$	−0.0813396	−	0.0813396i	−0.00702667	−	0.00702667i
$135$	−1.38481	−	1.75564i	−0.119186	−	0.151102i
$136$		−	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	$-0.674794\pi$
$139$	−12.3073			−1.04390			−0.521948	+	0.852977i	$0.674794\pi$
$140$	6.69198	−	5.27849i	0.565575	−	0.446114i
$141$		−	4.43682i		−	0.373648i
$142$	9.73699			0.817110
$143$			4.13069i			0.345426i
$144$		−	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
$148$	6.03268	−	0.778980i	0.495883	−	0.0640317i
$149$		−	18.0558i		−	1.47919i	−0.673052	−	0.739596i	$-0.735017\pi$
$149$		−	18.0558i		−	1.47919i	0.673052	−	0.739596i	$-0.264983\pi$
$150$	4.26178	−	2.61482i	0.347973	−	0.213499i
$151$			0.527274i			0.0429089i	0.999770	+	0.0214545i	$0.00682969\pi$
$151$			0.527274i			0.0429089i	−0.999770	+	0.0214545i	$0.993170\pi$
$152$	−4.87828	−	4.87828i	−0.395681	−	0.395681i
$153$	3.12620			0.252739
$154$	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
$162$	1.00000			0.0785674
$163$		−	16.8338i		−	1.31852i	−0.751914	−	0.659262i	$-0.770869\pi$
$163$		−	16.8338i		−	1.31852i	0.751914	−	0.659262i	$-0.229131\pi$
$164$		−	9.24361i		−	0.721805i
$165$	5.33747	+	6.76676i	0.415522	+	0.526792i
$166$	5.06491	+	5.06491i	0.393113	+	0.393113i
$167$			19.7919i			1.53154i	0.643112	+	0.765772i	$0.277643\pi$
$167$			19.7919i			1.53154i	−0.643112	+	0.765772i	$0.722357\pi$
$168$			3.81169i			0.294079i
$169$	−11.8514			−0.911648
$170$	−0.819742	+	6.94217i	−0.0628714	+	0.532440i
$171$	4.87828	−	4.87828i	0.373052	−	0.373052i
$172$	−8.98058			−0.684762
$173$	−11.9282	+	11.9282i	−0.906886	+	0.906886i	−0.996020	−	0.0891340i	$-0.971590\pi$
$173$	−11.9282	+	11.9282i	−0.906886	+	0.906886i	0.0891340	+	0.996020i	$0.471590\pi$
$174$			0.339781i			0.0257587i
$175$	−16.2446	+	9.96687i	−1.22798	+	0.753425i
$176$			3.85429i			0.290528i
$177$	−1.46558			−0.110160
$178$	−4.92656	+	4.92656i	−0.369262	+	0.369262i
$179$	−6.14221	+	6.14221i	−0.459090	+	0.459090i	−0.898357	−	0.439266i	$-0.855238\pi$
$179$	−6.14221	+	6.14221i	−0.459090	+	0.459090i	0.439266	+	0.898357i	$0.355238\pi$
$180$	−0.262217	+	2.22064i	−0.0195445	+	0.165517i
$181$	−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
$183$	−13.2029			−0.975989
$184$	6.72404			0.495702
$185$	−13.6007	+	0.147965i	−0.999941	+	0.0108786i
$186$	−10.3182			−0.756570
$187$	−12.0493			−0.881131
$188$	−3.13731	+	3.13731i	−0.228811	+	0.228811i
$189$	−3.81169			−0.277260
$190$	9.55375	+	12.1121i	0.693102	+	0.878703i
$191$	11.4031	−	11.4031i	0.825101	−	0.825101i	−0.161734	−	0.986834i	$-0.551709\pi$
$191$	11.4031	−	11.4031i	0.825101	−	0.825101i	0.986834	+	0.161734i	$0.0517086\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	25.7217			1.85149			0.925744	−	0.378150i	$-0.123440\pi$
$193$	25.7217			1.85149			0.925744	+	0.378150i	$0.123440\pi$
$194$		−	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	$0.245239\pi$
$198$	−3.85429			−0.273912
$199$	−5.41052	+	5.41052i	−0.383541	+	0.383541i	−0.872376	−	0.488835i	$-0.837422\pi$
$199$	−5.41052	+	5.41052i	−0.383541	+	0.383541i	0.488835	+	0.872376i	$0.337422\pi$
$200$	−4.86248	−	1.16458i	−0.343830	−	0.0823481i
$201$	−0.115032			−0.00811370
$202$			15.9490i			1.12217i
$203$		−	1.29514i		−	0.0909010i
$204$	−2.21056	−	2.21056i	−0.154770	−	0.154770i
$205$	−2.42383	+	20.5267i	−0.169287	+	1.43365i
$206$			7.78216i			0.542209i
$207$			6.72404i			0.467353i
$208$	1.07171			0.0743100
$209$	−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
$217$	39.3300			2.66989
$218$	8.01624	+	8.01624i	0.542929	+	0.542929i
$219$			5.33291i			0.360365i
$220$	1.01066	−	8.55899i	0.0681386	−	0.577047i
$221$			3.35039i			0.225372i
$222$	3.71492	−	4.81657i	0.249329	−	0.323267i
$223$	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
$227$		−	16.0147i		−	1.06293i	−0.847080	−	0.531465i	$-0.821642\pi$
$227$		−	16.0147i		−	1.06293i	0.847080	−	0.531465i	$-0.178358\pi$
$228$	−6.89894			−0.456893
$229$		−	9.95500i		−	0.657845i	−0.944357	−	0.328923i	$-0.893314\pi$
$229$		−	9.95500i		−	0.657845i	0.944357	−	0.328923i	$-0.106686\pi$
$230$	−14.9317	−	1.76315i	−0.984565	−	0.116259i
$231$	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	$0.524839\pi$
$233$	−16.4078	+	16.4078i	−1.07491	+	1.07491i	−0.996957	+	0.0779551i	$0.975161\pi$
$234$			1.07171i			0.0700601i
$235$	7.78948	−	6.14417i	0.508130	−	0.400802i
$236$	1.03632	+	1.03632i	0.0674590	+	0.0674590i
$237$	−6.13722			−0.398655
$238$	8.42597	+	8.42597i	0.546175	+	0.546175i
$239$	16.5390	+	16.5390i	1.06982	+	1.06982i	0.997372	+	0.0724452i	$0.0230802\pi$
$239$	16.5390	+	16.5390i	1.06982	+	1.06982i	0.0724452	+	0.997372i	$0.476920\pi$
$240$	1.75564	−	1.38481i	0.113326	−	0.0893894i
$241$	−9.38903	+	9.38903i	−0.604801	+	0.604801i	−0.941583	−	0.336782i	$-0.890662\pi$
$241$	−9.38903	+	9.38903i	−0.604801	+	0.604801i	0.336782	+	0.941583i	$0.390662\pi$
$242$	3.85554			0.247844
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	9.33589	+	9.33589i	0.597669	+	0.597669i
$245$	−1.97423	+	16.7192i	−0.126129	+	1.06815i
$246$	−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	0.508474	−	0.861077i	$-0.330210\pi$
$251$	−5.58629	−	5.58629i	−0.352603	−	0.352603i	−0.861077	+	0.508474i	$0.830210\pi$
$252$	2.69527	+	2.69527i	0.169786	+	0.169786i
$253$		−	25.9164i		−	1.62935i
$254$	−4.73530	+	4.73530i	−0.297119	+	0.297119i
$255$	4.32921	+	5.48850i	0.271106	+	0.343703i
$256$	1.00000			0.0625000
$257$			10.1055i			0.630365i	0.949031	+	0.315183i	$0.102066\pi$
$257$			10.1055i			0.630365i	−0.949031	+	0.315183i	$0.897934\pi$
$258$	−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	−0.198170	−	0.980168i	$-0.563500\pi$
$263$	12.6819	−	12.6819i	0.781998	−	0.781998i	0.980168	+	0.198170i	$0.0634998\pi$
$264$	2.72539	+	2.72539i	0.167736	+	0.167736i
$265$	13.2217	+	16.7622i	0.812200	+	1.02969i
$266$	26.2966			1.61235
$267$			6.96721i			0.426387i
$268$	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	$0.665028\pi$
$272$			3.12620i			0.189554i
$273$		−	4.08504i		−	0.247238i
$274$	−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
$277$	1.82943			0.109920			0.0549600	−	0.998489i	$-0.482497\pi$
$277$	1.82943			0.109920			0.0549600	+	0.998489i	$0.482497\pi$
$278$	12.3073			0.738146
$279$	−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	−0.913548	−	0.406732i	$-0.866668\pi$
$281$	−8.49578	+	8.49578i	−0.506816	+	0.506816i	0.406732	+	0.913548i	$0.366668\pi$
$282$			4.43682i			0.264209i
$283$			4.60113i			0.273509i	0.990605	+	0.136754i	$0.0436671\pi$
$283$			4.60113i			0.273509i	−0.990605	+	0.136754i	$0.956333\pi$
$284$	−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
$288$			1.00000i			0.0589256i
$289$	7.22686			0.425109
$290$	−0.596534	+	0.470533i	−0.0350297	+	0.0276307i
$291$	−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
$298$			18.0558i			1.04595i
$299$	−7.20624			−0.416748
$300$	−4.26178	+	2.61482i	−0.246054	+	0.150966i
$301$	24.2051	−	24.2051i	1.39516	−	1.39516i
$302$		−	0.527274i		−	0.0303412i
$303$	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	$-0.979447\pi$
$307$	−18.6155	−	18.6155i	−1.06244	−	1.06244i	−0.0645243	−	0.997916i	$-0.520553\pi$
$308$	−10.3884	−	10.3884i	−0.591932	−	0.591932i
$309$	5.50282	+	5.50282i	0.313044	+	0.313044i
$310$	−14.2888	−	18.1152i	−0.811552	−	1.02887i
$311$	1.28712	+	1.28712i	0.0729856	+	0.0729856i	0.742657	−	0.669672i	$-0.233565\pi$
$311$	1.28712	+	1.28712i	0.0729856	+	0.0729856i	−0.669672	+	0.742657i	$0.733565\pi$
$312$	0.757816	−	0.757816i	0.0429029	−	0.0429029i
$313$	−32.0767			−1.81308			−0.906540	−	0.422120i	$-0.861286\pi$
$313$	−32.0767			−1.81308			−0.906540	+	0.422120i	$0.861286\pi$
$314$	7.56393	−	7.56393i	0.426857	−	0.426857i
$315$	−5.27849	−	6.69198i	−0.297409	−	0.377050i
$316$	4.33967	+	4.33967i	0.244125	+	0.244125i
$317$	5.14557	+	5.14557i	0.289004	+	0.289004i	0.836686	−	0.547682i	$-0.184490\pi$
$317$	5.14557	+	5.14557i	0.289004	+	0.289004i	−0.547682	+	0.836686i	$0.684490\pi$
$318$	−9.54760			−0.535403
$319$	−0.926036	−	0.926036i	−0.0518481	−	0.0518481i
$320$	−2.22064	−	0.262217i	−0.124138	−	0.0146584i
$321$			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
$325$	5.21119	+	1.24809i	0.289065	+	0.0692318i
$326$			16.8338i			0.932337i
$327$	11.3367			0.626920
$328$			9.24361i			0.510393i
$329$		−	16.9118i		−	0.932377i
$330$	−5.33747	−	6.76676i	−0.293818	−	0.372498i
$331$	−8.41827	+	8.41827i	−0.462710	+	0.462710i	−0.899543	−	0.436833i	$-0.856100\pi$
$331$	−8.41827	+	8.41827i	−0.462710	+	0.462710i	0.436833	+	0.899543i	$0.356100\pi$
$332$	−5.06491	−	5.06491i	−0.277973	−	0.277973i
$333$	−0.778980	−	6.03268i	−0.0426878	−	0.330589i
$334$		−	19.7919i		−	1.08297i
$335$	−0.159297	−	0.201955i	−0.00870335	−	0.0110340i
$336$		−	3.81169i		−	0.207945i
$337$	5.24126	+	5.24126i	0.285510	+	0.285510i	0.835302	−	0.549792i	$-0.185293\pi$
$337$	5.24126	+	5.24126i	0.285510	+	0.285510i	−0.549792	+	0.835302i	$0.685293\pi$
$338$	11.8514			0.644633
$339$	−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
$347$	27.4976			1.47615			0.738074	−	0.674720i	$-0.235735\pi$
$347$	27.4976			1.47615			0.738074	+	0.674720i	$0.235735\pi$
$348$		−	0.339781i		−	0.0182142i
$349$		−	5.28646i		−	0.282978i	−0.989940	−	0.141489i	$-0.954811\pi$
$349$		−	5.28646i		−	0.282978i	0.989940	−	0.141489i	$-0.0451890\pi$
$350$	16.2446	−	9.96687i	0.868310	−	0.532752i
$351$	0.757816	+	0.757816i	0.0404492	+	0.0404492i
$352$		−	3.85429i		−	0.205434i
$353$		−	2.70748i		−	0.144105i	−0.997401	−	0.0720523i	$-0.977045\pi$
$353$		−	2.70748i		−	0.144105i	0.997401	−	0.0720523i	$-0.0229548\pi$
$354$	1.46558			0.0778949
$355$	21.6224	+	2.55320i	1.14760	+	0.135510i
$356$	4.92656	−	4.92656i	0.261107	−	0.261107i
$357$	11.9161			0.630668
$358$	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
$362$	11.3224			0.595092
$363$	2.72628	−	2.72628i	0.143093	−	0.143093i
$364$	−2.88856	+	2.88856i	−0.151402	+	0.151402i
$365$	−9.36269	+	7.38509i	−0.490066	+	0.386553i
$366$	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	$0.260194\pi$
$368$	−6.72404			−0.350515
$369$	−9.24361			−0.481203
$370$	13.6007	−	0.147965i	0.707065	−	0.00769235i
$371$	36.3925			1.88941
$372$	10.3182			0.534976
$373$	20.6119	−	20.6119i	1.06725	−	1.06725i	0.0696765	−	0.997570i	$-0.477803\pi$
$373$	20.6119	−	20.6119i	1.06725	−	1.06725i	0.997570	−	0.0696765i	$-0.0221967\pi$
$374$	12.0493			0.623054
$375$	10.1495	−	4.68905i	0.524119	−	0.242142i
$376$	3.13731	−	3.13731i	0.161794	−	0.161794i
$377$	−0.257491	+	0.257491i	−0.0132615	+	0.0132615i
$378$	3.81169			0.196052
$379$		−	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
$383$	5.14097			0.262691			0.131346	−	0.991337i	$-0.458070\pi$
$383$	5.14097			0.262691			0.131346	+	0.991337i	$0.458070\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	20.3448	+	25.7928i	1.03687	+	1.31452i
$386$	−25.7217			−1.30920
$387$			8.98058i			0.456508i
$388$			2.13394i			0.108334i
$389$	−13.7109	−	13.7109i	−0.695168	−	0.695168i	0.268196	−	0.963364i	$-0.413572\pi$
$389$	−13.7109	−	13.7109i	−0.695168	−	0.695168i	−0.963364	+	0.268196i	$0.913572\pi$
$390$	−1.88155	+	1.48412i	−0.0952759	+	0.0751516i
$391$		−	21.0207i		−	1.06306i
$392$			7.52901i			0.380272i
$393$	−14.4080			−0.726786
$394$	−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	$-0.959188\pi$
$397$	−22.3090	−	22.3090i	−1.11966	−	1.11966i	−0.127864	−	0.991792i	$-0.540812\pi$
$398$	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	0.841922	−	0.539599i	$-0.181424\pi$
$401$	6.05401	+	6.05401i	0.302323	+	0.302323i	−0.539599	+	0.841922i	$0.681424\pi$
$402$	0.115032			0.00573725
$403$	−7.81933	−	7.81933i	−0.389508	−	0.389508i
$404$		−	15.9490i		−	0.793494i
$405$	2.22064	+	0.262217i	0.110344	+	0.0130297i
$406$			1.29514i			0.0642767i
$407$	3.00241	+	23.2517i	0.148824	+	1.15254i
$408$	2.21056	+	2.21056i	0.109439	+	0.109439i
$409$	−6.83746	+	6.83746i	−0.338091	+	0.338091i	−0.855648	−	0.517558i	$-0.826841\pi$
$409$	−6.83746	+	6.83746i	−0.338091	+	0.338091i	0.517558	+	0.855648i	$0.326841\pi$
$410$	2.42383	−	20.5267i	0.119704	−	1.01374i
$411$			10.7092i			0.528245i
$412$		−	7.78216i		−	0.383399i
$413$	−5.58636			−0.274887
$414$		−	6.72404i		−	0.330468i
$415$	9.91924	+	12.5754i	0.486916	+	0.617304i
$416$	−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	$-0.0987613\pi$
$420$	−0.999489	+	8.46440i	−0.0487701	+	0.413020i
$421$	1.21803	+	1.21803i	0.0593634	+	0.0593634i	0.736165	−	0.676802i	$-0.236635\pi$
$421$	1.21803	+	1.21803i	0.0593634	+	0.0593634i	−0.676802	+	0.736165i	$0.736635\pi$
$422$	−14.5704			−0.709274
$423$	3.13731	+	3.13731i	0.152541	+	0.152541i
$424$	6.75117	+	6.75117i	0.327866	+	0.327866i
$425$	−3.64071	+	15.2011i	−0.176600	+	0.737362i
$426$	−6.88509	+	6.88509i	−0.333584	+	0.333584i
$427$	−50.3255			−2.43542
$428$	6.27687	−	6.27687i	0.303404	−	0.303404i
$429$	−2.92084	−	2.92084i	−0.141020	−	0.141020i
$430$	−19.9426	−	2.35486i	−0.961719	−	0.113561i
$431$	−12.0202	−	12.0202i	−0.578993	−	0.578993i	0.355633	−	0.934626i	$-0.384265\pi$
$431$	−12.0202	−	12.0202i	−0.578993	−	0.578993i	−0.934626	+	0.355633i	$0.884265\pi$
$432$	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
$438$		−	5.33291i		−	0.254816i
$439$	−3.20813	+	3.20813i	−0.153116	+	0.153116i	−0.779508	−	0.626392i	$-0.784531\pi$
$439$	−3.20813	+	3.20813i	−0.153116	+	0.153116i	0.626392	+	0.779508i	$0.284531\pi$
$440$	−1.01066	+	8.55899i	−0.0481813	+	0.408034i
$441$	−7.52901			−0.358524
$442$		−	3.35039i		−	0.159362i
$443$	7.74996	−	7.74996i	0.368211	−	0.368211i	−0.498613	−	0.866825i	$-0.666157\pi$
$443$	7.74996	−	7.74996i	0.368211	−	0.368211i	0.866825	+	0.498613i	$0.166157\pi$
$444$	−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	$-0.363590\pi$
$449$	−10.4682	−	10.4682i	−0.494024	−	0.494024i	−0.909571	+	0.415548i	$0.863590\pi$
$450$	−1.16458	+	4.86248i	−0.0548987	+	0.229220i
$451$	35.6275			1.67764
$452$			19.1057i			0.898658i
$453$	−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
$457$			1.41085i			0.0659970i	0.999455	+	0.0329985i	$0.0105057\pi$
$457$			1.41085i			0.0659970i	−0.999455	+	0.0329985i	$0.989494\pi$
$458$			9.95500i			0.465167i
$459$	−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	−0.983899	−	0.178726i	$-0.942802\pi$
$461$	−17.2878	+	17.2878i	−0.805173	+	0.805173i	0.178726	+	0.983899i	$0.442802\pi$
$462$	−14.6914			−0.683504
$463$	−27.9587			−1.29935			−0.649675	−	0.760212i	$-0.725095\pi$
$463$	−27.9587			−1.29935			−0.649675	+	0.760212i	$0.725095\pi$
$464$	−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
$467$			25.1108i			1.16199i	0.813907	+	0.580995i	$0.197336\pi$
$467$			25.1108i			1.16199i	−0.813907	+	0.580995i	$0.802664\pi$
$468$		−	1.07171i		−	0.0495400i
$469$	−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
$473$		−	34.6137i		−	1.59154i
$474$	6.13722			0.281892
$475$	18.0394	+	29.4017i	0.827706	+	1.34904i
$476$	−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	$-0.351169\pi$
$479$	−9.67259	−	9.67259i	−0.441952	−	0.441952i	−0.892668	+	0.450716i	$0.851169\pi$
$480$	−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
$483$			25.6300i			1.16620i
$484$	−3.85554			−0.175252
$485$	0.559554	−	4.73871i	0.0254080	−	0.215174i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			28.7468i			1.30264i	0.758803	+	0.651321i	$0.225785\pi$
$487$			28.7468i			1.30264i	−0.758803	+	0.651321i	$0.774215\pi$
$488$	−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
$495$	−8.55899	−	1.01066i	−0.384698	−	0.0454257i
$496$	−7.29610	−	7.29610i	−0.327604	−	0.327604i
$497$	26.2439	−	26.2439i	1.17720	−	1.17720i
$498$	−7.16286			−0.320976
$499$	−6.22662	+	6.22662i	−0.278742	+	0.278742i	−0.832607	−	0.553865i	$-0.813152\pi$
$499$	−6.22662	+	6.22662i	−0.278742	+	0.278742i	0.553865	+	0.832607i	$0.313152\pi$
$500$	−10.4925	−	3.86113i	−0.469237	−	0.172675i
$501$	−13.9950	−	13.9950i	−0.625251	−	0.625251i
$502$	5.58629	+	5.58629i	0.249328	+	0.249328i
$503$	−2.20186			−0.0981761			−0.0490880	−	0.998794i	$-0.515631\pi$
$503$	−2.20186			−0.0981761			−0.0490880	+	0.998794i	$0.515631\pi$
$504$	−2.69527	−	2.69527i	−0.120057	−	0.120057i
$505$	−4.18210	+	35.4171i	−0.186101	+	1.57604i
$506$			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	$-0.468542\pi$
$509$	4.45209			0.197335			0.0986677	+	0.995120i	$0.468542\pi$
$510$	−4.32921	−	5.48850i	−0.191701	−	0.243035i
$511$			20.3274i			0.899232i
$512$	−1.00000			−0.0441942
$513$			6.89894i			0.304595i
$514$		−	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
$518$	14.1602	−	18.3593i	0.622161	−	0.806661i
$519$		−	16.8690i		−	0.740469i
$520$	2.37989	+	0.281021i	0.104365	+	0.0123236i
$521$		−	3.61089i		−	0.158196i	−0.996867	−	0.0790979i	$-0.974796\pi$
$521$		−	3.61089i		−	0.158196i	0.996867	−	0.0790979i	$-0.0252040\pi$
$522$	−0.240261	−	0.240261i	−0.0105159	−	0.0105159i
$523$	−30.6225			−1.33903			−0.669514	−	0.742799i	$-0.733498\pi$
$523$	−30.6225			−1.33903			−0.669514	+	0.742799i	$0.733498\pi$
$524$	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
$532$	−26.2966			−1.14010
$533$		−	9.90650i		−	0.429098i
$534$		−	6.96721i		−	0.301501i
$535$	−15.5846	+	12.2928i	−0.673780	+	0.531463i
$536$	−0.0813396	−	0.0813396i	−0.00351334	−	0.00351334i
$537$		−	8.68640i		−	0.374846i
$538$		−	26.5570i		−	1.14495i
$539$	29.0190			1.24994
$540$	−1.38481	−	1.75564i	−0.0595929	−	0.0755509i
$541$	−28.0745	+	28.0745i	−1.20702	+	1.20702i	−0.235027	+	0.971989i	$0.575518\pi$
$541$	−28.0745	+	28.0745i	−1.20702	+	1.20702i	−0.971989	+	0.235027i	$0.924482\pi$
$542$	16.3151			0.700794
$543$	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
$547$	−20.4389			−0.873904			−0.436952	−	0.899485i	$-0.643942\pi$
$547$	−20.4389			−0.873904			−0.436952	+	0.899485i	$0.643942\pi$
$548$	7.57254	−	7.57254i	0.323483	−	0.323483i
$549$	9.33589	−	9.33589i	0.398446	−	0.398446i
$550$	4.48862	−	18.7414i	0.191395	−	0.799137i
$551$	−2.34412			−0.0998631
$552$	−4.75461	+	4.75461i	−0.202370	+	0.202370i
$553$	−23.3932			−0.994780
$554$	−1.82943			−0.0777252
$555$	9.51250	−	9.72175i	0.403783	−	0.412665i
$556$	−12.3073			−0.521948
$557$	39.1876			1.66043			0.830215	−	0.557443i	$-0.188217\pi$
$557$	39.1876			1.66043			0.830215	+	0.557443i	$0.188217\pi$
$558$	7.29610	−	7.29610i	0.308868	−	0.308868i
$559$	−9.62461			−0.407077
$560$	6.69198	−	5.27849i	0.282788	−	0.223057i
$561$	8.52013	−	8.52013i	0.359720	−	0.359720i
$562$	8.49578	−	8.49578i	0.358373	−	0.358373i
$563$	−15.3734			−0.647910			−0.323955	−	0.946073i	$-0.605013\pi$
$563$	−15.3734			−0.647910			−0.323955	+	0.946073i	$0.605013\pi$
$564$		−	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
$568$	9.73699			0.408555
$569$	11.9446	−	11.9446i	0.500743	−	0.500743i	−0.410925	−	0.911669i	$-0.634794\pi$
$569$	11.9446	−	11.9446i	0.500743	−	0.500743i	0.911669	+	0.410925i	$0.134794\pi$
$570$	−15.3201	−	1.80902i	−0.641686	−	0.0757713i
$571$	−19.6843			−0.823762			−0.411881	−	0.911238i	$-0.635128\pi$
$571$	−19.6843			−0.823762			−0.411881	+	0.911238i	$0.635128\pi$
$572$			4.13069i			0.172713i
$573$			16.1264i			0.673692i
$574$	−24.9141	−	24.9141i	−1.03989	−	1.03989i
$575$	−32.6955	−	7.83066i	−1.36350	−	0.326561i
$576$		−	1.00000i		−	0.0416667i
$577$		−	43.0027i		−	1.79022i	−0.445841	−	0.895112i	$-0.647095\pi$
$577$		−	43.0027i		−	1.79022i	0.445841	−	0.895112i	$-0.352905\pi$
$578$	−7.22686			−0.300598
$579$	−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
$587$	2.93901			0.121306			0.0606530	−	0.998159i	$-0.480682\pi$
$587$	2.93901			0.121306			0.0606530	+	0.998159i	$0.480682\pi$
$588$	5.32381	+	5.32381i	0.219550	+	0.219550i
$589$		−	71.1849i		−	2.93312i
$590$	2.02956	+	2.57304i	0.0835557	+	0.105931i
$591$			0.419872i			0.0172712i
$592$	6.03268	−	0.778980i	0.247941	−	0.0320159i
$593$	−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
$597$		−	7.65163i		−	0.313160i
$598$	7.20624			0.294685
$599$			37.7290i			1.54156i	0.637099	+	0.770782i	$0.280134\pi$
$599$			37.7290i			1.54156i	−0.637099	+	0.770782i	$0.719866\pi$
$600$	4.26178	−	2.61482i	0.173986	−	0.106749i
$601$	−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
$605$	8.56177	+	1.01099i	0.348085	+	0.0411025i
$606$	−11.2777	−	11.2777i	−0.458124	−	0.458124i
$607$	4.73701			0.192269			0.0961347	−	0.995368i	$-0.469352\pi$
$607$	4.73701			0.192269			0.0961347	+	0.995368i	$0.469352\pi$
$608$	−4.87828	−	4.87828i	−0.197841	−	0.197841i
$609$	0.915802	+	0.915802i	0.0371102	+	0.0371102i
$610$	18.2836	+	23.1797i	0.740282	+	0.938517i
$611$	−3.36229	+	3.36229i	−0.136024	+	0.136024i
$612$	3.12620			0.126369
$613$	7.31952	−	7.31952i	0.295633	−	0.295633i	−0.543668	−	0.839301i	$-0.682965\pi$
$613$	7.31952	−	7.31952i	0.295633	−	0.295633i	0.839301	+	0.543668i	$0.182965\pi$
$614$	18.6155	+	18.6155i	0.751259	+	0.751259i
$615$	−12.8007	−	16.2285i	−0.516173	−	0.654396i
$616$	10.3884	+	10.3884i	0.418559	+	0.418559i
$617$	−9.15306	−	9.15306i	−0.368488	−	0.368488i	0.498437	−	0.866926i	$-0.333907\pi$
$617$	−9.15306	−	9.15306i	−0.368488	−	0.368488i	−0.866926	+	0.498437i	$0.833907\pi$
$618$	−5.50282	−	5.50282i	−0.221356	−	0.221356i
$619$	19.9520			0.801939			0.400970	−	0.916091i	$-0.368673\pi$
$619$	19.9520			0.801939			0.400970	+	0.916091i	$0.368673\pi$
$620$	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
$623$			26.5569i			1.06398i
$624$	−0.757816	+	0.757816i	−0.0303369	+	0.0303369i
$625$	22.2875	+	11.3255i	0.891501	+	0.453019i
$626$	32.0767			1.28204
$627$		−	26.5905i		−	1.06192i
$628$	−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	0.528828	−	0.848729i	$-0.322631\pi$
$631$	−8.03580	−	8.03580i	−0.319900	−	0.319900i	−0.848729	+	0.528828i	$0.822631\pi$
$632$	−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
$635$	−11.7571	+	9.27372i	−0.466565	+	0.368016i
$636$	9.54760			0.378587
$637$		−	8.06894i		−	0.319703i
$638$	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	$0.541919\pi$
$642$		−	8.87684i		−	0.350341i
$643$		−	18.3325i		−	0.722963i	−0.932379	−	0.361481i	$-0.882271\pi$
$643$		−	18.3325i		−	0.722963i	0.932379	−	0.361481i	$-0.117729\pi$
$644$	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
$647$	31.8700			1.25294			0.626470	−	0.779445i	$-0.284499\pi$
$647$	31.8700			1.25294			0.626470	+	0.779445i	$0.284499\pi$
$648$	1.00000			0.0392837
$649$	−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
$652$		−	16.8338i		−	0.659262i
$653$		−	6.13141i		−	0.239941i	−0.992777	−	0.119970i	$-0.961720\pi$
$653$		−	6.13141i		−	0.239941i	0.992777	−	0.119970i	$-0.0382800\pi$
$654$	−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
$658$			16.9118i			0.659290i
$659$	9.15530			0.356640			0.178320	−	0.983973i	$-0.442934\pi$
$659$	9.15530			0.356640			0.178320	+	0.983973i	$0.442934\pi$
$660$	5.33747	+	6.76676i	0.207761	+	0.263396i
$661$	−6.95018	−	6.95018i	−0.270331	−	0.270331i	0.558903	−	0.829233i	$-0.311223\pi$
$661$	−6.95018	−	6.95018i	−0.270331	−	0.270331i	−0.829233	+	0.558903i	$0.811223\pi$
$662$	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
$668$			19.7919i			0.765772i
$669$	−10.8664			−0.420120
$670$	0.159297	+	0.201955i	0.00615420	+	0.00780219i
$671$	−35.9832	+	35.9832i	−1.38912	+	1.38912i
$672$			3.81169i			0.147039i
$673$	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	0.720256	−	0.693708i	$-0.244024\pi$
$677$	0.690751	+	0.690751i	0.0265477	+	0.0265477i	−0.693708	+	0.720256i	$0.744024\pi$
$678$	13.5098	+	13.5098i	0.518841	+	0.518841i
$679$	−5.75155	−	5.75155i	−0.220724	−	0.220724i
$680$	−0.819742	+	6.94217i	−0.0314357	+	0.266220i
$681$	11.3241	+	11.3241i	0.433940	+	0.433940i
$682$	−28.1213	+	28.1213i	−1.07682	+	1.07682i
$683$	−1.42429			−0.0544990			−0.0272495	−	0.999629i	$-0.508675\pi$
$683$	−1.42429			−0.0544990			−0.0272495	+	0.999629i	$0.508675\pi$
$684$	4.87828	−	4.87828i	0.186526	−	0.186526i
$685$	−18.8015	+	14.8302i	−0.718369	+	0.566634i
$686$	−1.42581	−	1.42581i	−0.0544378	−	0.0544378i
$687$	7.03925	+	7.03925i	0.268564	+	0.268564i
$688$	−8.98058			−0.342381
$689$	−7.23532	−	7.23532i	−0.275644	−	0.275644i
$690$	11.8050	−	9.31154i	0.449409	−	0.354484i
$691$			20.8427i			0.792894i	0.918058	+	0.396447i	$0.129757\pi$
$691$			20.8427i			0.792894i	−0.918058	+	0.396447i	$0.870243\pi$
$692$	−11.9282	+	11.9282i	−0.453443	+	0.453443i
$693$	−10.3884	+	10.3884i	−0.394621	+	0.394621i
$694$	−27.4976			−1.04379
$695$	27.3302	+	3.22719i	1.03669	+	0.122414i
$696$			0.339781i			0.0128794i
$697$	28.8974			1.09457
$698$			5.28646i			0.200096i
$699$		−	23.2042i		−	0.877662i
$700$	−16.2446	+	9.96687i	−0.613988	+	0.376712i
$701$	12.5457	−	12.5457i	0.473846	−	0.473846i	−0.429311	−	0.903157i	$-0.641244\pi$
$701$	12.5457	−	12.5457i	0.473846	−	0.473846i	0.903157	+	0.429311i	$0.141244\pi$
$702$	−0.757816	−	0.757816i	−0.0286019	−	0.0286019i
$703$	33.2292	+	25.6290i	1.25326	+	0.966617i
$704$			3.85429i			0.145264i
$705$	−1.16341	+	9.85258i	−0.0438165	+	0.371070i
$706$			2.70748i			0.101897i
$707$	42.9870	+	42.9870i	1.61669	+	1.61669i
$708$	−1.46558			−0.0550800
$709$	−31.0687	−	31.0687i	−1.16681	−	1.16681i	−0.982953	−	0.183856i	$-0.941142\pi$
$709$	−31.0687	−	31.0687i	−1.16681	−	1.16681i	−0.183856	−	0.982953i	$-0.558858\pi$
$710$	−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
$717$	−23.3896			−0.873502
$718$		−	20.4504i		−	0.763202i
$719$			4.08903i			0.152495i	0.997089	+	0.0762475i	$0.0242939\pi$
$719$			4.08903i			0.152495i	−0.997089	+	0.0762475i	$0.975706\pi$
$720$	−0.262217	+	2.22064i	−0.00977224	+	0.0827584i
$721$	20.9750	+	20.9750i	0.781151	+	0.781151i
$722$		−	28.5953i		−	1.06421i
$723$		−	13.2781i		−	0.493818i
$724$	−11.3224			−0.420793
$725$	−1.44807	+	0.888464i	−0.0537799	+	0.0329967i
$726$	−2.72628	+	2.72628i	−0.101182	+	0.101182i
$727$	4.10966			0.152419			0.0762094	−	0.997092i	$-0.475718\pi$
$727$	4.10966			0.152419			0.0762094	+	0.997092i	$0.475718\pi$
$728$	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
$732$	−13.2029			−0.487995
$733$	18.6280	−	18.6280i	0.688042	−	0.688042i	−0.273757	−	0.961799i	$-0.588266\pi$
$733$	18.6280	−	18.6280i	0.688042	−	0.688042i	0.961799	+	0.273757i	$0.0882663\pi$
$734$	0.867537	−	0.867537i	0.0320214	−	0.0320214i
$735$	−10.4263	−	13.2183i	−0.384579	−	0.487563i
$736$	6.72404			0.247851
$737$	−0.313506	+	0.313506i	−0.0115482	+	0.0115482i
$738$	9.24361			0.340262
$739$	14.2761			0.525154			0.262577	−	0.964911i	$-0.415428\pi$
$739$	14.2761			0.525154			0.262577	+	0.964911i	$0.415428\pi$
$740$	−13.6007	+	0.147965i	−0.499970	+	0.00543932i
$741$	−7.39368			−0.271614
$742$	−36.3925			−1.33601
$743$	16.7892	−	16.7892i	0.615937	−	0.615937i	−0.328550	−	0.944487i	$-0.606560\pi$
$743$	16.7892	−	16.7892i	0.615937	−	0.615937i	0.944487	+	0.328550i	$0.106560\pi$
$744$	−10.3182			−0.378285
$745$	−4.73454	+	40.0955i	−0.173460	+	1.46899i
$746$	−20.6119	+	20.6119i	−0.754657	+	0.754657i
$747$	−5.06491	+	5.06491i	−0.185315	+	0.185315i
$748$	−12.0493			−0.440566
$749$			33.8358i			1.23633i
$750$	−10.1495	+	4.68905i	−0.370608	+	0.171220i
$751$		−	29.4388i		−	1.07424i	−0.843506	−	0.537119i	$-0.819513\pi$
$751$		−	29.4388i		−	1.07424i	0.843506	−	0.537119i	$-0.180487\pi$
$752$	−3.13731	+	3.13731i	−0.114406	+	0.114406i
$753$	7.90020			0.287899
$754$	0.257491	−	0.257491i	0.00937728	−	0.00937728i
$755$	0.138260	−	1.17089i	0.00503180	−	0.0426129i
$756$	−3.81169			−0.138630
$757$			9.76824i			0.355033i	0.984118	+	0.177516i	$0.0568063\pi$
$757$			9.76824i			0.355033i	−0.984118	+	0.177516i	$0.943194\pi$
$758$			9.54382i			0.346647i
$759$	18.3256	+	18.3256i	0.665179	+	0.665179i
$760$	9.55375	+	12.1121i	0.346551	+	0.439351i
$761$			15.7759i			0.571875i	0.958248	+	0.285938i	$0.0923051\pi$
$761$			15.7759i			0.571875i	−0.958248	+	0.285938i	$0.907695\pi$
$762$		−	6.69672i		−	0.242597i
$763$	43.2120			1.56438
$764$	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	−0.0175316	+	0.999846i	$0.505581\pi$
$769$	−28.2128	+	28.2128i	−1.01738	+	1.01738i	−0.999846	+	0.0175316i	$0.994419\pi$
$770$	−20.3448	−	25.7928i	−0.733176	−	0.929509i
$771$	−7.14568	−	7.14568i	−0.257345	−	0.257345i
$772$	25.7217			0.925744
$773$	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
$775$	−26.9803	−	43.9740i	−0.969161	−	1.57959i
$776$		−	2.13394i		−	0.0766039i
$777$	−2.96923	−	22.9947i	−0.106521	−	0.824931i
$778$	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
$782$			21.0207i			0.751699i
$783$	−0.339781			−0.0121428
$784$		−	7.52901i		−	0.268893i
$785$	18.7802	−	14.8134i	0.670293	−	0.528712i
$786$	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
$790$	8.49891	+	10.7748i	0.302378	+	0.383349i
$791$	−51.4952	−	51.4952i	−1.83096	−	1.83096i
$792$	−3.85429			−0.136956
$793$	10.0054	+	10.0054i	0.355302	+	0.355302i
$794$	22.3090	+	22.3090i	0.791716	+	0.791716i
$795$	−21.2018	−	2.50354i	−0.751950	−	0.0887914i
$796$	−5.41052	+	5.41052i	−0.191771	+	0.191771i
$797$	0.184397			0.00653168			0.00326584	−	0.999995i	$-0.498960\pi$
$797$	0.184397			0.00653168			0.00326584	+	0.999995i	$0.498960\pi$
$798$	−18.5945	+	18.5945i	−0.658239	+	0.658239i
$799$	−9.80785	−	9.80785i	−0.346977	−	0.346977i
$800$	−4.86248	−	1.16458i	−0.171915	−	0.0411740i
$801$	−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
$808$			15.9490i			0.561085i
$809$	−18.7803	+	18.7803i	−0.660281	+	0.660281i	−0.955446	−	0.295165i	$-0.904625\pi$
$809$	−18.7803	+	18.7803i	−0.660281	+	0.660281i	0.295165	+	0.955446i	$0.404625\pi$
$810$	−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	$0.808077\pi$
$812$		−	1.29514i		−	0.0454505i
$813$	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
$820$	−2.42383	+	20.5267i	−0.0846437	+	0.716824i
$821$	19.7666			0.689859			0.344930	−	0.938629i	$-0.387903\pi$
$821$	19.7666			0.689859			0.344930	+	0.938629i	$0.387903\pi$
$822$		−	10.7092i		−	0.373526i
$823$	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
$827$		−	52.5723i		−	1.82812i	−0.405581	−	0.914059i	$-0.632931\pi$
$827$		−	52.5723i		−	1.82812i	0.405581	−	0.914059i	$-0.367069\pi$
$828$			6.72404i			0.233676i
$829$	−34.5891	+	34.5891i	−1.20133	+	1.20133i	−0.227568	+	0.973762i	$0.573077\pi$
$829$	−34.5891	+	34.5891i	−1.20133	+	1.20133i	−0.973762	+	0.227568i	$0.926923\pi$
$830$	−9.91924	−	12.5754i	−0.344302	−	0.436500i
$831$	−1.29360	+	1.29360i	−0.0448747	+	0.0448747i
$832$	1.07171			0.0371550
$833$	23.5372			0.815516
$834$	−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
$837$		−	10.3182i		−	0.356651i
$838$			12.4992i			0.431779i
$839$	16.5268			0.570568			0.285284	−	0.958443i	$-0.407912\pi$
$839$	16.5268			0.570568			0.285284	+	0.958443i	$0.407912\pi$
$840$	0.999489	−	8.46440i	0.0344857	−	0.292050i
$841$			28.8845i			0.996019i
$842$	−1.21803	−	1.21803i	−0.0419763	−	0.0419763i
$843$		−	12.0148i		−	0.413813i
$844$	14.5704			0.501532
$845$	26.3178	+	3.10764i	0.905358	+	0.106906i
$846$	−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
$853$		−	20.2197i		−	0.692309i	−0.938177	−	0.346155i	$-0.887487\pi$
$853$		−	20.2197i		−	0.692309i	0.938177	−	0.346155i	$-0.112513\pi$
$854$	50.3255			1.72210
$855$	−12.1121	+	9.55375i	−0.414224	+	0.326731i
$856$	−6.27687	+	6.27687i	−0.214539	+	0.214539i
$857$			26.0449i			0.889675i	0.895611	+	0.444838i	$0.146739\pi$
$857$			26.0449i			0.889675i	−0.895611	+	0.444838i	$0.853261\pi$
$858$	2.92084	+	2.92084i	0.0997159	+	0.0997159i
$859$	5.92987	+	5.92987i	0.202324	+	0.202324i	0.800995	−	0.598671i	$-0.204304\pi$
$859$	5.92987	+	5.92987i	0.202324	+	0.202324i	−0.598671	+	0.800995i	$0.704304\pi$
$860$	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
$865$	29.6161	−	23.3605i	1.00698	−	0.794281i
$866$	15.2027	+	15.2027i	0.516609	+	0.516609i
$867$	−5.11016	+	5.11016i	−0.173550	+	0.173550i
$868$	39.3300			1.33495
$869$	−16.7263	+	16.7263i	−0.567402	+	0.567402i
$870$	0.0890961	−	0.754530i	0.00302064	−	0.0255810i
$871$	0.0871728	+	0.0871728i	0.00295374	+	0.00295374i
$872$	8.01624	+	8.01624i	0.271464	+	0.271464i
$873$	2.13394			0.0722228
$874$	32.8018	+	32.8018i	1.10954	+	1.10954i
$875$	38.6869	−	17.8732i	1.30785	−	0.604226i
$876$			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
$880$	1.01066	−	8.55899i	0.0340693	−	0.288523i
$881$			7.99622i			0.269400i	0.990886	+	0.134700i	$0.0430070\pi$
$881$			7.99622i			0.269400i	−0.990886	+	0.134700i	$0.956993\pi$
$882$	7.52901			0.253515
$883$		−	25.8732i		−	0.870704i	−0.900260	−	0.435352i	$-0.856624\pi$
$883$		−	25.8732i		−	0.870704i	0.900260	−	0.435352i	$-0.143376\pi$
$884$			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	0.157478	−	0.987523i	$-0.449664\pi$
$887$	−24.7209	−	24.7209i	−0.830045	−	0.830045i	−0.987523	+	0.157478i	$0.949664\pi$
$888$	3.71492	−	4.81657i	0.124665	−	0.161633i
$889$			25.5258i			0.856109i
$890$	12.2320	−	9.64830i	0.410016	−	0.323412i
$891$		−	3.85429i		−	0.129124i
$892$	7.68371	+	7.68371i	0.257270	+	0.257270i
$893$	−30.6093			−1.02430
$894$	−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
$902$	−35.6275			−1.18627
$903$			34.2312i			1.13914i
$904$		−	19.1057i		−	0.635447i
$905$	25.1430	+	2.96892i	0.835780	+	0.0986902i
$906$	0.372839	+	0.372839i	0.0123867	+	0.0123867i
$907$			59.2927i			1.96878i	0.175992	+	0.984392i	$0.443687\pi$
$907$			59.2927i			1.96878i	−0.175992	+	0.984392i	$0.556313\pi$
$908$		−	16.0147i		−	0.531465i
$909$	−15.9490			−0.528996
$910$	−7.17189	+	5.65703i	−0.237746	+	0.187529i
$911$	2.95948	−	2.95948i	0.0980518	−	0.0980518i	−0.656379	−	0.754431i	$-0.727913\pi$
$911$	2.95948	−	2.95948i	0.0980518	−	0.0980518i	0.754431	+	0.656379i	$0.227913\pi$
$912$	−6.89894			−0.228447
$913$	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
$917$	−54.9187			−1.81358
$918$	2.21056	−	2.21056i	0.0729593	−	0.0729593i
$919$	−8.84725	+	8.84725i	−0.291844	+	0.291844i	−0.837808	−	0.545964i	$-0.816163\pi$
$919$	−8.84725	+	8.84725i	−0.291844	+	0.291844i	0.545964	+	0.837808i	$0.316163\pi$
$920$	−14.9317	−	1.76315i	−0.492282	−	0.0581295i
$921$	26.3262			0.867479
$922$	17.2878	−	17.2878i	0.569343	−	0.569343i
$923$	−10.4353			−0.343481
$924$	14.6914			0.483310
$925$	30.2410	+	3.23774i	0.994317	+	0.106456i
$926$	27.9587			0.918779
$927$	−7.78216			−0.255600
$928$	0.240261	−	0.240261i	0.00788696	−	0.00788696i
$929$	−20.1987			−0.662699			−0.331350	−	0.943508i	$-0.607504\pi$
$929$	−20.1987			−0.662699			−0.331350	+	0.943508i	$0.607504\pi$
$930$	22.9131	+	2.70561i	0.751350	+	0.0887206i
$931$	36.7286	−	36.7286i	1.20373	−	1.20373i
$932$	−16.4078	+	16.4078i	−0.537456	+	0.537456i
$933$	−1.82026			−0.0595925
$934$		−	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	$0.281650\pi$
$938$	0.438465			0.0143164
$939$	22.6816	−	22.6816i	0.740187	−	0.740187i
$940$	7.78948	−	6.14417i	0.254065	−	0.200401i
$941$	−28.1989			−0.919257			−0.459628	−	0.888111i	$-0.652017\pi$
$941$	−28.1989			−0.919257			−0.459628	+	0.888111i	$0.652017\pi$
$942$			10.6970i			0.348528i
$943$			62.1544i			2.02402i
$944$	1.03632	+	1.03632i	0.0337295	+	0.0337295i
$945$	8.46440	+	0.999489i	0.275347	+	0.0325134i
$946$			34.6137i			1.12539i
$947$			16.9403i			0.550486i	0.961375	+	0.275243i	$0.0887583\pi$
$947$			16.9403i			0.550486i	−0.961375	+	0.275243i	$0.911242\pi$
$948$	−6.13722			−0.199328
$949$	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	−0.583365	−	0.812210i	$-0.698264\pi$
$953$	7.06463	−	7.06463i	0.228846	−	0.228846i	0.812210	+	0.583365i	$0.198264\pi$
$954$	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
$957$	1.30961			0.0423338
$958$	9.67259	+	9.67259i	0.312507	+	0.312507i
$959$			40.8201i			1.31815i
$960$	1.75564	−	1.38481i	0.0566632	−	0.0446947i
$961$			75.4661i			2.43439i
$962$	−6.46530	+	0.834843i	−0.208450	+	0.0269164i
$963$	−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
$967$		−	26.0501i		−	0.837716i	−0.908052	−	0.418858i	$-0.862431\pi$
$967$		−	26.0501i		−	0.837716i	0.908052	−	0.418858i	$-0.137569\pi$
$968$	3.85554			0.123922
$969$		−	21.5675i		−	0.692847i
$970$	−0.559554	+	4.73871i	−0.0179662	+	0.152151i
$971$	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
$975$	−4.56740	+	2.80233i	−0.146274	+	0.0897465i
$976$	9.33589	+	9.33589i	0.298834	+	0.298834i
$977$	−11.5254			−0.368730			−0.184365	−	0.982858i	$-0.559023\pi$
$977$	−11.5254			−0.368730			−0.184365	+	0.982858i	$0.559023\pi$
$978$	−11.9033	−	11.9033i	−0.380625	−	0.380625i
$979$	18.9884	+	18.9884i	0.606872	+	0.606872i
$980$	−1.97423	+	16.7192i	−0.0630645	+	0.534076i
$981$	−8.01624	+	8.01624i	−0.255939	+	0.255939i
$982$	17.9127			0.571619
$983$	−28.2941	+	28.2941i	−0.902442	+	0.902442i	−0.995647	−	0.0932046i	$-0.970289\pi$
$983$	−28.2941	+	28.2941i	−0.902442	+	0.902442i	0.0932046	+	0.995647i	$0.470289\pi$
$984$	−6.53622	−	6.53622i	−0.208367	−	0.208367i
$985$	−0.737146	+	0.581444i	−0.0234874	+	0.0185264i
$986$	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	0.647052	−	0.762446i	$-0.276002\pi$
$991$	−3.63262	−	3.63262i	−0.115394	−	0.115394i	−0.762446	+	0.647052i	$0.776002\pi$
$992$	7.29610	+	7.29610i	0.231651	+	0.231651i
$993$		−	11.9052i		−	0.377801i
$994$	−26.2439	+	26.2439i	−0.832405	+	0.832405i
$995$	13.4335	−	10.5961i	0.425872	−	0.335918i
$996$	7.16286			0.226964
$997$			55.1711i			1.74729i	0.486567	+	0.873644i	$0.338249\pi$
$997$			55.1711i			1.74729i	−0.486567	+	0.873644i	$0.661751\pi$
$998$	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.o.a.253.2	yes	36
5.2	odd	4		1110.2.l.a.697.18	yes	36
37.6	odd	4		1110.2.l.a.43.18	✓	36
185.117	even	4	inner	1110.2.o.a.487.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.18	✓	36	37.6	odd	4
1110.2.l.a.697.18	yes	36	5.2	odd	4
1110.2.o.a.253.2	yes	36	1.1	even	1	trivial
1110.2.o.a.487.2	yes	36	185.117	even	4	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more