LMFDB - Embedded newform 1110.2.o.a.487.2

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			487.2
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.2

$q$-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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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	−0.999821	−	0.0188964i	$-0.993985\pi$
$7$	−2.69527	−	2.69527i	−1.01872	−	1.01872i	−0.0188964	−	0.999821i	$-0.506015\pi$
$8$	−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	$-0.802640\pi$
$11$		−	3.85429i		−	1.16211i	0.813864	−	0.581056i	$-0.197360\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	1.07171			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	$-0.876231\pi$
$17$		−	3.12620i		−	0.758216i	0.925353	−	0.379108i	$-0.123769\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.87828	−	4.87828i	1.11916	−	1.11916i	0.127289	−	0.991866i	$-0.459372\pi$
$19$	4.87828	−	4.87828i	1.11916	−	1.11916i	0.991866	−	0.127289i	$-0.0406277\pi$
$20$	−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	0.684447	−	0.729063i	$-0.260044\pi$
$29$	−0.240261	−	0.240261i	−0.0446154	−	0.0446154i	−0.729063	+	0.684447i	$0.760044\pi$
$30$	−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	$0.872713\pi$
$32$	−1.00000			−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	$0.256687\pi$
$41$			9.24361i			1.44361i	−0.692097	+	0.721805i	$0.743313\pi$
$42$		−	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	0.440252	−	0.897874i	$-0.354889\pi$
$47$	−3.13731	−	3.13731i	−0.457623	−	0.457623i	−0.897874	+	0.440252i	$0.854889\pi$
$48$	−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	−0.997534	−	0.0701888i	$-0.977640\pi$
$53$	−6.75117	+	6.75117i	−0.927345	+	0.927345i	0.0701888	+	0.997534i	$0.477640\pi$
$54$	−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	−0.636423	−	0.771341i	$-0.719587\pi$
$59$	1.03632	−	1.03632i	0.134918	−	0.134918i	0.771341	+	0.636423i	$0.219587\pi$
$60$	1.75564	+	1.38481i	0.226653	+	0.178779i
$61$	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	$-0.747763\pi$
$67$	0.0813396	−	0.0813396i	0.00993722	−	0.00993722i	0.712058	+	0.702121i	$0.247763\pi$
$68$		−	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	0.892467	−	0.451112i	$-0.148973\pi$
$73$	3.77094	+	3.77094i	0.441355	+	0.441355i	−0.451112	+	0.892467i	$0.648973\pi$
$74$	−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	−0.419503	−	0.907754i	$-0.637796\pi$
$79$	4.33967	−	4.33967i	0.488251	−	0.488251i	0.907754	+	0.419503i	$0.137796\pi$
$80$	−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	−0.928151	−	0.372205i	$-0.878602\pi$
$83$	−5.06491	+	5.06491i	−0.555946	+	0.555946i	0.372205	+	0.928151i	$0.378602\pi$
$84$			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	0.918240	−	0.396025i	$-0.129611\pi$
$89$	4.92656	+	4.92656i	0.522215	+	0.522215i	−0.396025	+	0.918240i	$0.629611\pi$
$90$	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	$-0.965448\pi$
$97$		−	2.13394i		−	0.216668i	0.994115	−	0.108334i	$-0.0345517\pi$
$98$		−	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	$0.291740\pi$
$101$			15.9490i			1.58699i	−0.608578	+	0.793494i	$0.708260\pi$
$102$	2.21056	−	2.21056i	0.218878	−	0.218878i
$103$			7.78216i			0.766799i	0.923583	+	0.383399i	$0.125247\pi$
$103$			7.78216i			0.766799i	−0.923583	+	0.383399i	$0.874753\pi$
$104$	−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	0.942111	−	0.335302i	$-0.108838\pi$
$107$	6.27687	+	6.27687i	0.606808	+	0.606808i	−0.335302	+	0.942111i	$0.608838\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−8.01624	+	8.01624i	−0.767817	+	0.767817i	−0.977722	−	0.209905i	$-0.932685\pi$
$109$	−8.01624	+	8.01624i	−0.767817	+	0.767817i	0.209905	+	0.977722i	$0.432685\pi$
$110$	−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	$-0.644543\pi$
$113$		−	19.1057i		−	1.79732i	0.438650	−	0.898658i	$-0.355457\pi$
$114$	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	0.885269	−	0.465079i	$-0.153974\pi$
$127$	4.73530	+	4.73530i	0.420190	+	0.420190i	−0.465079	+	0.885269i	$0.653974\pi$
$128$	−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	−0.104408	−	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
$133$	−26.2966			−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	0.952258	−	0.305293i	$-0.0987544\pi$
$137$	7.57254	+	7.57254i	0.646965	+	0.646965i	−0.305293	+	0.952258i	$0.598754\pi$
$138$	−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	$0.264983\pi$
$149$			18.0558i			1.47919i	−0.673052	+	0.739596i	$0.735017\pi$
$150$	4.26178	+	2.61482i	0.347973	+	0.213499i
$151$		−	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
$153$	3.12620			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	0.337616	−	0.941284i	$-0.390379\pi$
$157$	−7.56393	−	7.56393i	−0.603668	−	0.603668i	−0.941284	+	0.337616i	$0.890379\pi$
$158$	−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	$0.229131\pi$
$163$			16.8338i			1.31852i	−0.751914	+	0.659262i	$0.770869\pi$
$164$			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	$-0.722357\pi$
$167$		−	19.7919i		−	1.53154i	0.643112	−	0.765772i	$-0.277643\pi$
$168$		−	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	0.0891340	−	0.996020i	$-0.471590\pi$
$173$	−11.9282	−	11.9282i	−0.906886	−	0.906886i	−0.996020	+	0.0891340i	$0.971590\pi$
$174$		−	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	0.439266	−	0.898357i	$-0.355238\pi$
$179$	−6.14221	−	6.14221i	−0.459090	−	0.459090i	−0.898357	+	0.439266i	$0.855238\pi$
$180$	−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	0.986834	−	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
$193$	25.7217			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	0.717604	−	0.696451i	$-0.245239\pi$
$197$	0.296894	+	0.296894i	0.0211528	+	0.0211528i	−0.696451	+	0.717604i	$0.745239\pi$
$198$	−3.85429			−0.273912
$199$	−5.41052	−	5.41052i	−0.383541	−	0.383541i	0.488835	−	0.872376i	$-0.337422\pi$
$199$	−5.41052	−	5.41052i	−0.383541	−	0.383541i	−0.872376	+	0.488835i	$0.837422\pi$
$200$	−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	−0.401374	−	0.915914i	$-0.631467\pi$
$223$	7.68371	−	7.68371i	0.514540	−	0.514540i	0.915914	+	0.401374i	$0.131467\pi$
$224$	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	$0.178358\pi$
$227$			16.0147i			1.06293i	−0.847080	+	0.531465i	$0.821642\pi$
$228$	−6.89894			−0.456893
$229$			9.95500i			0.657845i	0.944357	+	0.328923i	$0.106686\pi$
$229$			9.95500i			0.657845i	−0.944357	+	0.328923i	$0.893314\pi$
$230$	−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	−0.996957	−	0.0779551i	$-0.975161\pi$
$233$	−16.4078	−	16.4078i	−1.07491	−	1.07491i	−0.0779551	−	0.996957i	$-0.524839\pi$
$234$		−	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	0.0724452	−	0.997372i	$-0.476920\pi$
$239$	16.5390	−	16.5390i	1.06982	−	1.06982i	0.997372	−	0.0724452i	$-0.0230802\pi$
$240$	1.75564	+	1.38481i	0.113326	+	0.0893894i
$241$	−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	$0.890662\pi$
$242$	3.85554			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	−0.861077	−	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
$253$			25.9164i			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	$-0.897934\pi$
$257$		−	10.1055i		−	0.630365i	0.949031	−	0.315183i	$-0.102066\pi$
$258$	−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	$-0.0634998\pi$
$263$	12.6819	+	12.6819i	0.781998	+	0.781998i	−0.198170	+	0.980168i	$0.563500\pi$
$264$	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	$-0.699682\pi$
$269$		−	26.5570i		−	1.61921i	0.586978	−	0.809603i	$-0.300318\pi$
$270$	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	0.406732	−	0.913548i	$-0.366668\pi$
$281$	−8.49578	−	8.49578i	−0.506816	−	0.506816i	−0.913548	+	0.406732i	$0.866668\pi$
$282$		−	4.43682i		−	0.264209i
$283$		−	4.60113i		−	0.273509i	−0.990605	−	0.136754i	$-0.956333\pi$
$283$		−	4.60113i		−	0.273509i	0.990605	−	0.136754i	$-0.0436671\pi$
$284$	−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	−0.867154	−	0.498041i	$-0.834053\pi$
$293$	−6.31819	+	6.31819i	−0.369113	+	0.369113i	0.498041	+	0.867154i	$0.334053\pi$
$294$	−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	−0.0645243	+	0.997916i	$0.520553\pi$
$307$	−18.6155	+	18.6155i	−1.06244	+	1.06244i	−0.997916	+	0.0645243i	$0.979447\pi$
$308$	−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	−0.669672	−	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
$313$	−32.0767			−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	−0.547682	−	0.836686i	$-0.684490\pi$
$317$	5.14557	−	5.14557i	0.289004	−	0.289004i	0.836686	+	0.547682i	$0.184490\pi$
$318$	−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	0.436833	−	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
$333$	−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	−0.549792	−	0.835302i	$-0.685293\pi$
$337$	5.24126	−	5.24126i	0.285510	−	0.285510i	0.835302	+	0.549792i	$0.185293\pi$
$338$	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	$0.0451890\pi$
$349$			5.28646i			0.282978i	−0.989940	+	0.141489i	$0.954811\pi$
$350$	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	$0.0229548\pi$
$353$			2.70748i			0.144105i	−0.997401	+	0.0720523i	$0.977045\pi$
$354$	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	$-0.818551\pi$
$359$		−	20.4504i		−	1.07933i	0.841880	−	0.539665i	$-0.181449\pi$
$360$	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	0.684102	−	0.729387i	$-0.260194\pi$
$367$	−0.867537	−	0.867537i	−0.0452851	−	0.0452851i	−0.729387	+	0.684102i	$0.760194\pi$
$368$	−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	0.997570	+	0.0696765i	$0.0221967\pi$
$373$	20.6119	+	20.6119i	1.06725	+	1.06725i	0.0696765	+	0.997570i	$0.477803\pi$
$374$	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	$0.0788263\pi$
$379$			9.54382i			0.490233i	−0.969494	+	0.245117i	$0.921174\pi$
$380$	−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	−0.963364	−	0.268196i	$-0.913572\pi$
$389$	−13.7109	+	13.7109i	−0.695168	+	0.695168i	0.268196	+	0.963364i	$0.413572\pi$
$390$	−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	−0.127864	+	0.991792i	$0.540812\pi$
$397$	−22.3090	+	22.3090i	−1.11966	+	1.11966i	−0.991792	+	0.127864i	$0.959188\pi$
$398$	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	$0.181424\pi$
$402$	0.115032			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	0.517558	−	0.855648i	$-0.326841\pi$
$409$	−6.83746	−	6.83746i	−0.338091	−	0.338091i	−0.855648	+	0.517558i	$0.826841\pi$
$410$	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	$0.0987613\pi$
$419$			12.4992i			0.610627i	−0.952252	+	0.305314i	$0.901239\pi$
$420$	−0.999489	−	8.46440i	−0.0487701	−	0.413020i
$421$	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	$0.236635\pi$
$422$	−14.5704			−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	−0.934626	−	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	−0.970738	−	0.240142i	$-0.922806\pi$
$433$	−15.2027	+	15.2027i	−0.730596	+	0.730596i	0.240142	+	0.970738i	$0.422806\pi$
$434$	−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	0.626392	−	0.779508i	$-0.284531\pi$
$439$	−3.20813	−	3.20813i	−0.153116	−	0.153116i	−0.779508	+	0.626392i	$0.784531\pi$
$440$	−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	0.866825	−	0.498613i	$-0.166157\pi$
$443$	7.74996	+	7.74996i	0.368211	+	0.368211i	−0.498613	+	0.866825i	$0.666157\pi$
$444$	−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	−0.909571	−	0.415548i	$-0.863590\pi$
$449$	−10.4682	+	10.4682i	−0.494024	+	0.494024i	0.415548	+	0.909571i	$0.363590\pi$
$450$	−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	$-0.989494\pi$
$457$		−	1.41085i		−	0.0659970i	0.999455	−	0.0329985i	$-0.0105057\pi$
$458$		−	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	0.178726	−	0.983899i	$-0.442802\pi$
$461$	−17.2878	−	17.2878i	−0.805173	−	0.805173i	−0.983899	+	0.178726i	$0.942802\pi$
$462$	−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	$-0.802664\pi$
$467$		−	25.1108i		−	1.16199i	0.813907	−	0.580995i	$-0.197336\pi$
$468$			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	−0.892668	−	0.450716i	$-0.851169\pi$
$479$	−9.67259	+	9.67259i	−0.441952	+	0.441952i	0.450716	+	0.892668i	$0.351169\pi$
$480$	−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	$-0.774215\pi$
$487$		−	28.7468i		−	1.30264i	0.758803	−	0.651321i	$-0.225785\pi$
$488$	−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	0.553865	−	0.832607i	$-0.313152\pi$
$499$	−6.22662	−	6.22662i	−0.278742	−	0.278742i	−0.832607	+	0.553865i	$0.813152\pi$
$500$	−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	$0.0252040\pi$
$521$			3.61089i			0.158196i	−0.996867	+	0.0790979i	$0.974796\pi$
$522$	−0.240261	+	0.240261i	−0.0105159	+	0.0105159i
$523$	−30.6225			−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	−0.971989	−	0.235027i	$-0.924482\pi$
$541$	−28.0745	−	28.0745i	−1.20702	−	1.20702i	−0.235027	−	0.971989i	$-0.575518\pi$
$542$	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	0.911669	−	0.410925i	$-0.134794\pi$
$569$	11.9446	+	11.9446i	0.500743	+	0.500743i	−0.410925	+	0.911669i	$0.634794\pi$
$570$	−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	$0.352905\pi$
$577$			43.0027i			1.79022i	−0.445841	+	0.895112i	$0.647095\pi$
$578$	−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	−0.367359	+	0.930079i	$0.619738\pi$
$593$	−31.5947	+	31.5947i	−1.29744	+	1.29744i	−0.930079	+	0.367359i	$0.880262\pi$
$594$	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	$-0.719866\pi$
$599$		−	37.7290i		−	1.54156i	0.637099	−	0.770782i	$-0.280134\pi$
$600$	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	0.839301	−	0.543668i	$-0.182965\pi$
$613$	7.31952	+	7.31952i	0.295633	+	0.295633i	−0.543668	+	0.839301i	$0.682965\pi$
$614$	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	−0.866926	−	0.498437i	$-0.833907\pi$
$617$	−9.15306	+	9.15306i	−0.368488	+	0.368488i	0.498437	+	0.866926i	$0.333907\pi$
$618$	−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	−0.848729	−	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
$635$	−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	$0.117729\pi$
$643$			18.3325i			0.722963i	−0.932379	+	0.361481i	$0.882271\pi$
$644$	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	$0.0382800\pi$
$653$			6.13141i			0.239941i	−0.992777	+	0.119970i	$0.961720\pi$
$654$	−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	−0.829233	−	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
$668$		−	19.7919i		−	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	−0.463240	−	0.886233i	$-0.653313\pi$
$673$	10.9734	−	10.9734i	0.422993	−	0.422993i	0.886233	+	0.463240i	$0.153313\pi$
$674$	−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	$-0.744024\pi$
$677$	0.690751	−	0.690751i	0.0265477	−	0.0265477i	0.720256	+	0.693708i	$0.244024\pi$
$678$	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	$-0.870243\pi$
$691$		−	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
$695$	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	0.903157	−	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
$703$	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	−0.183856	+	0.982953i	$0.558858\pi$
$709$	−31.0687	+	31.0687i	−1.16681	+	1.16681i	−0.982953	+	0.183856i	$0.941142\pi$
$710$	−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	$-0.975706\pi$
$719$		−	4.08903i		−	0.152495i	0.997089	−	0.0762475i	$-0.0242939\pi$
$720$	−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	0.961799	−	0.273757i	$-0.0882663\pi$
$733$	18.6280	+	18.6280i	0.688042	+	0.688042i	−0.273757	+	0.961799i	$0.588266\pi$
$734$	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	0.944487	−	0.328550i	$-0.106560\pi$
$743$	16.7892	+	16.7892i	0.615937	+	0.615937i	−0.328550	+	0.944487i	$0.606560\pi$
$744$	−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	$0.180487\pi$
$751$			29.4388i			1.07424i	−0.843506	+	0.537119i	$0.819513\pi$
$752$	−3.13731	−	3.13731i	−0.114406	−	0.114406i
$753$	7.90020			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	$-0.943194\pi$
$757$		−	9.76824i		−	0.355033i	0.984118	−	0.177516i	$-0.0568063\pi$
$758$		−	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	$-0.907695\pi$
$761$		−	15.7759i		−	0.571875i	0.958248	−	0.285938i	$-0.0923051\pi$
$762$			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	−0.999846	−	0.0175316i	$-0.994419\pi$
$769$	−28.2128	−	28.2128i	−1.01738	−	1.01738i	−0.0175316	−	0.999846i	$-0.505581\pi$
$770$	−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	−0.0489203	−	0.998803i	$-0.515578\pi$
$773$	26.4095	−	26.4095i	0.949882	−	0.949882i	0.998803	+	0.0489203i	$0.0155780\pi$
$774$			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	0.780151	−	0.625592i	$-0.215142\pi$
$787$	4.33592	+	4.33592i	0.154559	+	0.154559i	−0.625592	+	0.780151i	$0.715142\pi$
$788$	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	0.295165	−	0.955446i	$-0.404625\pi$
$809$	−18.7803	−	18.7803i	−0.660281	−	0.660281i	−0.955446	+	0.295165i	$0.904625\pi$
$810$	−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	−0.488612	−	0.872501i	$-0.662497\pi$
$823$	11.0130	−	11.0130i	0.383889	−	0.383889i	0.872501	+	0.488612i	$0.162497\pi$
$824$		−	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	$0.367069\pi$
$827$			52.5723i			1.82812i	−0.405581	+	0.914059i	$0.632931\pi$
$828$		−	6.72404i		−	0.233676i
$829$	−34.5891	−	34.5891i	−1.20133	−	1.20133i	−0.973762	−	0.227568i	$-0.926923\pi$
$829$	−34.5891	−	34.5891i	−1.20133	−	1.20133i	−0.227568	−	0.973762i	$-0.573077\pi$
$830$	−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	$0.112513\pi$
$853$			20.2197i			0.692309i	−0.938177	+	0.346155i	$0.887487\pi$
$854$	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	$-0.853261\pi$
$857$		−	26.0449i		−	0.889675i	0.895611	−	0.444838i	$-0.146739\pi$
$858$	2.92084	−	2.92084i	0.0997159	−	0.0997159i
$859$	5.92987	−	5.92987i	0.202324	−	0.202324i	−0.598671	−	0.800995i	$-0.704304\pi$
$859$	5.92987	−	5.92987i	0.202324	−	0.202324i	0.800995	+	0.598671i	$0.204304\pi$
$860$	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	−0.966949	−	0.254969i	$-0.917935\pi$
$863$	−20.9158	+	20.9158i	−0.711980	+	0.711980i	0.254969	+	0.966949i	$0.417935\pi$
$864$	−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	0.791724	−	0.610879i	$-0.209184\pi$
$877$	5.35557	+	5.35557i	0.180845	+	0.180845i	−0.610879	+	0.791724i	$0.709184\pi$
$878$	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	$-0.956993\pi$
$881$		−	7.99622i		−	0.269400i	0.990886	−	0.134700i	$-0.0430070\pi$
$882$	7.52901			0.253515
$883$			25.8732i			0.870704i	0.900260	+	0.435352i	$0.143376\pi$
$883$			25.8732i			0.870704i	−0.900260	+	0.435352i	$0.856624\pi$
$884$		−	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	$-0.949664\pi$
$887$	−24.7209	+	24.7209i	−0.830045	+	0.830045i	0.157478	+	0.987523i	$0.449664\pi$
$888$	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	$-0.556313\pi$
$907$		−	59.2927i		−	1.96878i	0.175992	−	0.984392i	$-0.443687\pi$
$908$			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	0.754431	−	0.656379i	$-0.227913\pi$
$911$	2.95948	+	2.95948i	0.0980518	+	0.0980518i	−0.656379	+	0.754431i	$0.727913\pi$
$912$	−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	0.545964	−	0.837808i	$-0.316163\pi$
$919$	−8.84725	−	8.84725i	−0.291844	−	0.291844i	−0.837808	+	0.545964i	$0.816163\pi$
$920$	−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	0.633421	−	0.773808i	$-0.281650\pi$
$937$	−4.29731	−	4.29731i	−0.140387	−	0.140387i	−0.773808	+	0.633421i	$0.781650\pi$
$938$	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	$-0.911242\pi$
$947$		−	16.9403i		−	0.550486i	0.961375	−	0.275243i	$-0.0887583\pi$
$948$	−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	0.812210	−	0.583365i	$-0.198264\pi$
$953$	7.06463	+	7.06463i	0.228846	+	0.228846i	−0.583365	+	0.812210i	$0.698264\pi$
$954$	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	$0.137569\pi$
$967$			26.0501i			0.837716i	−0.908052	+	0.418858i	$0.862431\pi$
$968$	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	0.0932046	−	0.995647i	$-0.470289\pi$
$983$	−28.2941	−	28.2941i	−0.902442	−	0.902442i	−0.995647	+	0.0932046i	$0.970289\pi$
$984$	−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	−0.762446	−	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
$993$			11.9052i			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	$-0.661751\pi$
$997$		−	55.1711i		−	1.74729i	0.486567	−	0.873644i	$-0.338249\pi$
$998$	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.487.2	yes	36
5.3	odd	4		1110.2.l.a.43.18	✓	36
37.31	odd	4		1110.2.l.a.697.18	yes	36
185.68	even	4	inner	1110.2.o.a.253.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.18	✓	36	5.3	odd	4
1110.2.l.a.697.18	yes	36	37.31	odd	4
1110.2.o.a.253.2	yes	36	185.68	even	4	inner
1110.2.o.a.487.2	yes	36	1.1	even	1	trivial

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

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